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<!--Created on: 6/17/2026 12:36:46 AM-->
<!--Modified on: 6/17/2026 12:36:46 AM-->
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryNet" xlink:to="us-gaap_InventoryNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventories, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_InventoryNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetsCurrent" xlink:label="us-gaap_DerivativeAssetsCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeAssetsCurrent" xlink:to="us-gaap_DerivativeAssetsCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Asset, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Forward purchase agreement derivative asset</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_WorkingCapitalAdvancesCurrentDebitInstant" xlink:label="cntm_WorkingCapitalAdvancesCurrentDebitInstant" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_WorkingCapitalAdvancesCurrentDebitInstant" xlink:to="cntm_WorkingCapitalAdvancesCurrentDebitInstant_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_WorkingCapitalAdvancesCurrentDebitInstant_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of working capital advances within a period of one year.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_WorkingCapitalAdvancesCurrentDebitInstant_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Working Capital Advances Current Debit/Instant</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_WorkingCapitalAdvancesCurrentDebitInstant_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Working capital advances</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:to="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepaid Expense and Other Assets, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepaid expenses and other current assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsCurrent" xlink:label="us-gaap_AssetsCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsCurrent" xlink:to="us-gaap_AssetsCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total current assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAsset" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Right-of-Use Asset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-use asset - operating lease</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-use asset - operating lease</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseRightOfUseAsset" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseRightOfUseAsset" xlink:to="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Right-of-Use Asset, after Accumulated Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-use asset - finance lease</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-use asset - finance lease</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentNet" xlink:label="us-gaap_PropertyPlantAndEquipmentNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentNet" xlink:to="us-gaap_PropertyPlantAndEquipmentNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property and equipment, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Goodwill" xlink:label="us-gaap_Goodwill" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Goodwill" xlink:to="us-gaap_Goodwill_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Goodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_Goodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill, Ending Balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_Goodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill, Beginning Balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Goodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:to="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Assets, Net (Excluding Goodwill)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible assets, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proprietary know-how and technical documents</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestments" xlink:label="us-gaap_EquityMethodInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestments" xlink:to="us-gaap_EquityMethodInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity method investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment in Sun Solar</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Assets" xlink:to="us-gaap_Assets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Assets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Assets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_Assets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total Assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities and Equity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities and Stockholders' Deficit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities and Stockholders' Deficit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesCurrentAbstract" xlink:label="us-gaap_LiabilitiesCurrentAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="us-gaap_LiabilitiesCurrentAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities, Current [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableCurrent" xlink:label="us-gaap_AccountsPayableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsPayableCurrent" xlink:to="us-gaap_AccountsPayableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Payable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:label="us-gaap_AccruedLiabilitiesAndOtherLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:to="us-gaap_AccruedLiabilitiesAndOtherLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccruedLiabilitiesAndOtherLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued Liabilities and Other Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccruedLiabilitiesAndOtherLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued expenses and other current liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LiabilityForContingentConsiderationCurrent" xlink:label="cntm_LiabilityForContingentConsiderationCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LiabilityForContingentConsiderationCurrent" xlink:to="cntm_LiabilityForContingentConsiderationCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LiabilityForContingentConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of liability recognized arising from contingent consideration within one year.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LiabilityForContingentConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liability For Contingent Consideration Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LiabilityForContingentConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansPayableCurrent" xlink:label="us-gaap_LoansPayableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LoansPayableCurrent" xlink:to="us-gaap_LoansPayableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LoansPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loans Payable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LoansPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt, net of debt discount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConvertibleNotesPayableCurrent" xlink:label="us-gaap_ConvertibleNotesPayableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConvertibleNotesPayableCurrent" xlink:to="us-gaap_ConvertibleNotesPayableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConvertibleNotesPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes Payable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConvertibleNotesPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible debt, at fair value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ConvertibleNotesPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible notes payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilitiesCurrent" xlink:label="us-gaap_DerivativeLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeLiabilitiesCurrent" xlink:to="us-gaap_DerivativeLiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of derivative liabilities associated with share reset adjustment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DerivativeLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DeferredConsiderationCurrent" xlink:label="cntm_DeferredConsiderationCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DeferredConsiderationCurrent" xlink:to="cntm_DeferredConsiderationCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DeferredConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of deferred consideration,  expected to be settled within one year or normal operating cycle.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DeferredConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Consideration, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DeferredConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_DeferredConsiderationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Consideration</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityCurrent" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilityCurrent" xlink:to="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityCurrent" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityCurrent" xlink:to="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance lease liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerLiabilityCurrent" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractWithCustomerLiabilityCurrent" xlink:to="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SettlementAgreementFairValueDisclosure" xlink:label="cntm_SettlementAgreementFairValueDisclosure" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementAgreementFairValueDisclosure" xlink:to="cntm_SettlementAgreementFairValueDisclosure_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAgreementFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value portion of settlement agreement for shares issued under Section 3(a)(10) of the Securities Act.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementAgreementFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Agreement, Fair Value Disclosure</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAgreementFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">3(a)(10) Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_SettlementAgreementFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">3(a)(10) Settlement Agreement, at fair value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesCurrent" xlink:label="us-gaap_OtherLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherLiabilitiesCurrent" xlink:to="us-gaap_OtherLiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DeferredIncomeTaxLiabilitiesCurrent" xlink:label="cntm_DeferredIncomeTaxLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DeferredIncomeTaxLiabilitiesCurrent" xlink:to="cntm_DeferredIncomeTaxLiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DeferredIncomeTaxLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount represents deferred income tax liabilities current.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DeferredIncomeTaxLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Income Tax Liabilities Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DeferredIncomeTaxLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred tax liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesCurrent" xlink:label="us-gaap_LiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_LiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total current liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermNotesPayable" xlink:label="us-gaap_LongTermNotesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermNotesPayable" xlink:to="us-gaap_LongTermNotesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payable, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt, net of current portion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:to="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Liability, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease liabilities, net of current portion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:to="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Liability, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance lease liabilities, net of current portion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xlink:to="us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Liability, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration liability, net of current portion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities" xlink:label="us-gaap_Liabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_Liabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Liabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_Liabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingencies" xlink:label="us-gaap_CommitmentsAndContingencies" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsAndContingencies" xlink:to="us-gaap_CommitmentsAndContingencies_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments and Contingencies</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments and Contingencies (Note 11)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments and Contingencies</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityAbstract" xlink:label="us-gaap_StockholdersEquityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityAbstract" xlink:to="us-gaap_StockholdersEquityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity, Attributable to Parent [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Deficit:</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Deficit:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockValue" xlink:label="us-gaap_PreferredStockValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockValue" xlink:to="us-gaap_PreferredStockValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Value, Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock Series A, $0.0001 par value, 10,000,000 shares authorized as of December 31, 2025 and December 31, 2024 no shares issued or outstanding as of December 31, 2025 and December 31, 2024</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock Series A, $0.0001 par value, 10,000,000 shares authorized as of March 31, 2026 and December 31, 2025 no shares issued or outstanding as of March 31, 2026 and December 31, 2025</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockValue" xlink:label="us-gaap_CommonStockValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockValue" xlink:to="us-gaap_CommonStockValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Value, Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, $0.001 par value, 250,000,000 shares authorized as of March 31, 2026 and December 31, 2025, 5,312,911 and 4,789,230 issued and outstanding as of March 31, 2026 and December 31, 2025 respectively</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, $0.0001 par value, 250,000,000 shares and 100,000,000 shares authorized as of December 31, 2025 and December 31, 2024 respectively, 4,789,230 and 909,165 issued and outstanding as of December 31, 2025 and December 31, 2024 respectively</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapital" xlink:label="us-gaap_AdditionalPaidInCapital" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Paid in Capital</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_StockholdersEquity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity, Attributable to Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_StockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total ConnectM Technology Solutions, Inc.'s stockholders' deficit</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterest" xlink:to="us-gaap_MinorityInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MinorityInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-controlling interest</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquity" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities and Equity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total liabilities and stockholders' deficit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SeriesAPreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series A Preferred Stock [Member]</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockParOrStatedValuePerShare" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Par or Stated Value Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred shares, par value (in dollars per share)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock, par value (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesAuthorized" xlink:label="us-gaap_PreferredStockSharesAuthorized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesAuthorized" xlink:to="us-gaap_PreferredStockSharesAuthorized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Shares Authorized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred shares, shares authorized (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock, shares authorized (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesIssued" xlink:label="us-gaap_PreferredStockSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesIssued" xlink:to="us-gaap_PreferredStockSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Shares Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock, shares issued (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesOutstanding" xlink:label="us-gaap_PreferredStockSharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesOutstanding" xlink:to="us-gaap_PreferredStockSharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Shares Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock, shares outstanding (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Par or Stated Value Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, par value (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorized" xlink:label="us-gaap_CommonStockSharesAuthorized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesAuthorized" xlink:to="us-gaap_CommonStockSharesAuthorized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares Authorized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, stock authorized (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, shares authorized (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued" xlink:label="us-gaap_CommonStockSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, shares issued (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding" xlink:label="us-gaap_CommonStockSharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Outstanding</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostOfRevenue" xlink:label="us-gaap_CostOfRevenue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostOfRevenue" xlink:to="us-gaap_CostOfRevenue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostOfRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cost of Revenue</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CostOfRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cost of revenues</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GrossProfit" xlink:label="us-gaap_GrossProfit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GrossProfit" xlink:to="us-gaap_GrossProfit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GrossProfit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross Profit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_GrossProfit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross profit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SellingGeneralAndAdministrativeExpense" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SellingGeneralAndAdministrativeExpense" xlink:to="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, General and Administrative Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, general and administrative expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total selling, general and administrative expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingIncomeLoss" xlink:label="us-gaap_OperatingIncomeLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingIncomeLoss" xlink:to="us-gaap_OperatingIncomeLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Income (Loss)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">(Loss) income from operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss from operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">(Loss) income from operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonoperatingIncomeExpenseAbstract" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="us-gaap_NonoperatingIncomeExpenseAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nonoperating Income (Expense) [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other income (expense):</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseNonoperating" xlink:label="us-gaap_InterestExpenseNonoperating" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestExpenseNonoperating" xlink:to="us-gaap_InterestExpenseNonoperating_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Expense, Nonoperating</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest expense</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LossOnIssuanceOfFinancialInstruments" xlink:label="cntm_LossOnIssuanceOfFinancialInstruments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LossOnIssuanceOfFinancialInstruments" xlink:to="cntm_LossOnIssuanceOfFinancialInstruments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LossOnIssuanceOfFinancialInstruments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of discount or loss on issuance of financial instruments.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LossOnIssuanceOfFinancialInstruments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss On Issuance Of Financial Instruments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_LossOnIssuanceOfFinancialInstruments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on issuance of financial instruments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LossOnIssuanceOfFinancialInstruments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on issuance of financial instruments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable" xlink:label="cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable" xlink:to="cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of gain or loss from difference between the fair value of payments made and the carrying amount of debt and vendor payable which is extinguished prior to maturity during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) On Extinguishment Of Debt And Vendor Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GainLossOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on extinguishment of debt and vendor payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GainOnExtinguishmentOfDebt" xlink:label="cntm_GainOnExtinguishmentOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GainOnExtinguishmentOfDebt" xlink:to="cntm_GainOnExtinguishmentOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GainOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain recognized during the period upon extinguishment of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GainOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain On Extinguishment of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_GainOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on extinguishment of debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_GainOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on extinguishment of debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueMeasurementOfDebtUnrealizedGainLoss" xlink:label="cntm_FairValueMeasurementOfDebtUnrealizedGainLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementOfDebtUnrealizedGainLoss" xlink:to="cntm_FairValueMeasurementOfDebtUnrealizedGainLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementOfDebtUnrealizedGainLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of unrealized gain (loss) on fair value measurement of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementOfDebtUnrealizedGainLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Measurement of Debt, Unrealized Gain (Loss)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueMeasurementOfDebtUnrealizedGainLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of convertible debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreement" xlink:label="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreement" xlink:to="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The net change in the difference between the fair value and the carrying value, or in the comparative fair values, of forward purchase agreement put option liabilities, held at each balance sheet date, that was included in earnings for the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrealized Gain (Loss) on Derivatives, Liabilities, Forward Purchase Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of forward purchase agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xlink:label="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xlink:to="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration Arrangements, Change in Amount of Contingent Consideration, Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of contingent consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of contingent contingent consideration</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GainLossOnInitialRecognitionOfDebtAndConvertibleNotes" xlink:label="cntm_GainLossOnInitialRecognitionOfDebtAndConvertibleNotes" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GainLossOnInitialRecognitionOfDebtAndConvertibleNotes" xlink:to="cntm_GainLossOnInitialRecognitionOfDebtAndConvertibleNotes_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GainLossOnInitialRecognitionOfDebtAndConvertibleNotes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of gain (loss) on initial recognition of debt instruments including convertible notes by the entity during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GainLossOnInitialRecognitionOfDebtAndConvertibleNotes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) On Initial Recognition Of Debt And Convertible Notes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GainLossOnInitialRecognitionOfDebtAndConvertibleNotes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Day one gain on issuance of SEPA</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnDerivatives" xlink:label="us-gaap_UnrealizedGainLossOnDerivatives" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UnrealizedGainLossOnDerivatives" xlink:to="us-gaap_UnrealizedGainLossOnDerivatives_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UnrealizedGainLossOnDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrealized Gain (Loss) on Derivatives</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_UnrealizedGainLossOnDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of forward purchase agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_UnrealizedGainLossOnDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of derivative liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UnrealizedGainLossOnDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value gain</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_UnrealizedGainLossOnDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of derivative liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LossOnForwardPurchaseAgreement" xlink:label="cntm_LossOnForwardPurchaseAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LossOnForwardPurchaseAgreement" xlink:to="cntm_LossOnForwardPurchaseAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LossOnForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of loss on termination on forward purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LossOnForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss On Forward Purchase Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LossOnForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on forward purchase agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GainOnForwardPurchaseAgreement" xlink:label="cntm_GainOnForwardPurchaseAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GainOnForwardPurchaseAgreement" xlink:to="cntm_GainOnForwardPurchaseAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GainOnForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain on modifications to forward purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GainOnForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain On Forward Purchase Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GainOnForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on forward purchase agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GainLossOnModificationOfLiabilities" xlink:label="cntm_GainLossOnModificationOfLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount" xlink:label="cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount" xlink:to="cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of gain (loss) recognized from bargain purchase under business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Bargain Purchase, Gain (Loss) Recognized Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bargain purchase gain</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationBargainPurchaseGainLossRecognizedAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bargain purchase gain</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement" xlink:label="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement" xlink:to="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expense (income) related to adjustment to fair value of shares settled liability under settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Adjustment of Other Payables, Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value on Section 3(a)(10) Settlement Agreement (Note 9)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value on Section 3(a)(10) Settlement Agreement (Note 12)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of 3(a)(10) Settlement Agreement (Note 9)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_FairValueAdjustmentOfOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of Section 3(a)(10) Settlement Agreement (Note 12)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromEquityMethodInvestments" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeLossFromEquityMethodInvestments" xlink:to="us-gaap_IncomeLossFromEquityMethodInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (Loss) from Equity Method Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity in earnings from Sun Solar</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity in earnings from Sun Solar</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:to="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Not Discontinued Operation, Gain (Loss) on Disposal</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on disposal of businesses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on disposal of businesses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNonoperatingIncomeExpense" xlink:label="us-gaap_OtherNonoperatingIncomeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherNonoperatingIncomeExpense" xlink:to="us-gaap_OtherNonoperatingIncomeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Nonoperating Income (Expense)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other income (expense), net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonoperatingIncomeExpense" xlink:label="us-gaap_NonoperatingIncomeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NonoperatingIncomeExpense" xlink:to="us-gaap_NonoperatingIncomeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nonoperating Income (Expense)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other income (expense), net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total other income (expense), net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other (expense) income, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit" xlink:label="us-gaap_IncomeTaxExpenseBenefit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxExpenseBenefit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax Expense (Benefit)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income tax benefit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income tax provision</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total income taxes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProfitLoss" xlink:label="us-gaap_ProfitLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProfitLoss" xlink:to="us-gaap_ProfitLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProfitLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_ProfitLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_ProfitLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProfitLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:to="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Income (Loss) Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: net income attributable to noncontrolling interests</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: net income (loss) attributable to noncontrolling interests</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_NetIncomeLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Income (Loss)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss attributable to ConnectM Technology Solutions, Inc.</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTaxAbstract" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComprehensiveIncomeNetOfTaxAbstract" xlink:to="us-gaap_ComprehensiveIncomeNetOfTaxAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income (Loss), Net of Tax, Attributable to Parent [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other comprehensive income (loss):</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Foreign currency translation adjustments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other comprehensive income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:to="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income (Loss), Net of Tax, Including Portion Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive loss before noncontrolling interests</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:to="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: comprehensive income attributable to non-controlling interests</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Number of Shares Outstanding, Basic</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted average shares outstanding of common stock, basic (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Number of Shares Outstanding, Diluted</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted average shares outstanding of common stock, diluted ( in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareBasic" xlink:label="us-gaap_EarningsPerShareBasic" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareBasic" xlink:to="us-gaap_EarningsPerShareBasic_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Basic</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basic net loss per share, common stock ( in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDiluted" xlink:label="us-gaap_EarningsPerShareDiluted" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Diluted</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Diluted net loss per share, common stock ( in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfStockholdersEquityAbstract" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CONDENSED CONSOLIDATED STATEMENTS OF STOCKHOLDERS' DEFICIT</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis" xlink:label="us-gaap_StatementEquityComponentsAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementEquityComponentsAxis" xlink:to="us-gaap_StatementEquityComponentsAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Components [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain" xlink:label="us-gaap_EquityComponentDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityComponentDomain" xlink:to="us-gaap_EquityComponentDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityComponentDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Component [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ParentMember" xlink:label="us-gaap_ParentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ParentMember" xlink:to="us-gaap_ParentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ParentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Parent [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ParentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Deficit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember" xlink:label="us-gaap_CommonStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockMember" xlink:to="us-gaap_CommonStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapitalMember" xlink:label="us-gaap_AdditionalPaidInCapitalMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdditionalPaidInCapitalMember" xlink:to="us-gaap_AdditionalPaidInCapitalMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Paid-in Capital [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Paid-In Capital</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsMember" xlink:label="us-gaap_RetainedEarningsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RetainedEarningsMember" xlink:to="us-gaap_RetainedEarningsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RetainedEarningsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Retained Earnings [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RetainedEarningsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated Deficit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AOCI Attributable to Parent [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated Other Comprehensive Income (Loss)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncontrollingInterestMember" xlink:label="us-gaap_NoncontrollingInterestMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncontrollingInterestMember" xlink:to="us-gaap_NoncontrollingInterestMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis" xlink:label="us-gaap_BusinessAcquisitionAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionAxis" xlink:to="us-gaap_BusinessAcquisitionAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Acquiree [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AirTempServiceCoInc.AndSolarEnergySystemsOfBrevardIncMember" xlink:label="cntm_AirTempServiceCoInc.AndSolarEnergySystemsOfBrevardIncMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AirTempServiceCoInc.AndSolarEnergySystemsOfBrevardIncMember" xlink:to="cntm_AirTempServiceCoInc.AndSolarEnergySystemsOfBrevardIncMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AirTempServiceCoInc.AndSolarEnergySystemsOfBrevardIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Air Temp Service Co, Inc. ("Air Temp") and Solar Energy Systems of Brevard, Inc ("SES").</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AirTempServiceCoInc.AndSolarEnergySystemsOfBrevardIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Air Temp Service Co, Inc. and Solar Energy Systems of Brevard, Inc [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_AirTempServiceCoInc.AndSolarEnergySystemsOfBrevardIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ATS and SESB</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CambridgeEnergyResourcesLtdMember" xlink:label="cntm_CambridgeEnergyResourcesLtdMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CambridgeEnergyResourcesLtdMember" xlink:to="cntm_CambridgeEnergyResourcesLtdMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CambridgeEnergyResourcesLtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information related to Cambridge Energy Resources Ltd</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CambridgeEnergyResourcesLtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cambridge Energy Resources Ltd [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_CambridgeEnergyResourcesLtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CER</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GlobalImpexLlcMember" xlink:label="cntm_GlobalImpexLlcMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GlobalImpexLlcMember" xlink:to="cntm_GlobalImpexLlcMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GlobalImpexLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Global Impex LLC.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GlobalImpexLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Global Impex LLC [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GlobalImpexLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Global Impex LLC</label>
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    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AmpericsHoldingsLlcMember" xlink:label="cntm_AmpericsHoldingsLlcMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AmpericsHoldingsLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to asset acquisition of Amperics Holdings LLC.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AmpericsHoldingsLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amperics Holdings LLC [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AmpericsHoldingsLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amperics Holdings LLC</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentAxis" xlink:to="us-gaap_DebtInstrumentAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain" xlink:label="us-gaap_DebtInstrumentNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentNameDomain" xlink:to="us-gaap_DebtInstrumentNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConvertibleDebtMember" xlink:label="us-gaap_ConvertibleDebtMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConvertibleDebtMember" xlink:to="us-gaap_ConvertibleDebtMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConvertibleDebtMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Debt [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConvertibleDebtMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertiblePromissoryNotesMember" xlink:label="cntm_ConvertiblePromissoryNotesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertiblePromissoryNotesMember" xlink:to="cntm_ConvertiblePromissoryNotesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertiblePromissoryNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to convertible promissory notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertiblePromissoryNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Promissory Notes [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertiblePromissoryNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible promissory notes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Stockholders' Equity [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Stockholders' Equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharesOutstanding" xlink:label="us-gaap_SharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharesOutstanding" xlink:to="us-gaap_SharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares, Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_SharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_SharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares outstanding</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodValueCommitmentSharesUponAcquisitionOfConvertibleDebt" xlink:label="cntm_StockIssuedDuringPeriodValueCommitmentSharesUponAcquisitionOfConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueCommitmentSharesUponAcquisitionOfConvertibleDebt" xlink:to="cntm_StockIssuedDuringPeriodValueCommitmentSharesUponAcquisitionOfConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueCommitmentSharesUponAcquisitionOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of commitment shares issued in connection with the acquisition of convertible debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueCommitmentSharesUponAcquisitionOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Commitment Shares, Upon Acquisition Of Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueCommitmentSharesUponAcquisitionOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of commitment shares in connection with convertible debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodSharesCommitmentSharesUponAcquisitionOfConvertibleDebt" xlink:label="cntm_StockIssuedDuringPeriodSharesCommitmentSharesUponAcquisitionOfConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesCommitmentSharesUponAcquisitionOfConvertibleDebt" xlink:to="cntm_StockIssuedDuringPeriodSharesCommitmentSharesUponAcquisitionOfConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesCommitmentSharesUponAcquisitionOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of commitment shares issued in connection with the acquisition of convertible debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesCommitmentSharesUponAcquisitionOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Commitment Shares, Upon Acquisition Of Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesCommitmentSharesUponAcquisitionOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of commitment shares in connection with convertible debt (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodValueSettlementAgreement" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueSettlementAgreement" xlink:to="cntm_StockIssuedDuringPeriodValueSettlementAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of stock issued during the period as part of settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to settle claim under Section 3(a)10 Settlement Agreement ( see Note 9)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to settle claim under Section 3(a)10 Settlement Agreement (see Note 12)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodSharesSettlementAgreement" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesSettlementAgreement" xlink:to="cntm_StockIssuedDuringPeriodSharesSettlementAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of stock issued during the period as part of settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to settle claim under Section 3(a)10 Settlement Agreement ( see Note 9) (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to settle claim</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities" xlink:to="cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of stock issued to settle share reset derivative liabilities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Issued for Share Reset Derivative Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to settle share reset derivative liabilities (see Note 10)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to settle share reset derivative liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities" xlink:to="cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued to settle share reset derivative liabilities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Issued for Share Reset Derivative Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to settle share reset derivative liabilities (see Note 10) (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to settle share reset derivative liabilities (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, New Issues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, New Issues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of Representative Shares (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ShareIssuedDuringPeriodValueAcquisitionsRecapitalizationNet" xlink:label="cntm_ShareIssuedDuringPeriodValueAcquisitionsRecapitalizationNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ShareIssuedDuringPeriodValueAcquisitionsRecapitalizationNet" xlink:to="cntm_ShareIssuedDuringPeriodValueAcquisitionsRecapitalizationNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ShareIssuedDuringPeriodValueAcquisitionsRecapitalizationNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of shares issued in connection with business combination recapitalization, net of transaction costs.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ShareIssuedDuringPeriodValueAcquisitionsRecapitalizationNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Issued During Period, Value, Acquisitions, Recapitalization, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ShareIssuedDuringPeriodValueAcquisitionsRecapitalizationNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination with MCAC, net of transaction costs</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ShareIssuedDuringPeriodSharesAcquisitionsRecapitalizationNet" xlink:label="cntm_ShareIssuedDuringPeriodSharesAcquisitionsRecapitalizationNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ShareIssuedDuringPeriodSharesAcquisitionsRecapitalizationNet" xlink:to="cntm_ShareIssuedDuringPeriodSharesAcquisitionsRecapitalizationNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ShareIssuedDuringPeriodSharesAcquisitionsRecapitalizationNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination recapitalization net of transaction costs (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ShareIssuedDuringPeriodSharesAcquisitionsRecapitalizationNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Issued During Period, Shares, Acquisitions, Recapitalization, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ShareIssuedDuringPeriodSharesAcquisitionsRecapitalizationNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination with MCAC, net of transaction costs (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:label="us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination" xlink:to="us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest, Increase from Business Combination</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NoncontrollingInterestIncreaseFromBusinessCombination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition of noncontrolling interest in connection with acquisition of a business</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:label="us-gaap_StockIssuedDuringPeriodValueAcquisitions" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:to="us-gaap_StockIssuedDuringPeriodValueAcquisitions_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodValueAcquisitions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Acquisitions</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodValueAcquisitions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock as consideration in acquisition of a business</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:to="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Acquisitions</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock as consideration in acquisition of a business (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AdjustmentsToAdditionalPaidInCapitalChangeInMinorityOwnershipInterest" xlink:label="cntm_AdjustmentsToAdditionalPaidInCapitalChangeInMinorityOwnershipInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AdjustmentsToAdditionalPaidInCapitalChangeInMinorityOwnershipInterest" xlink:to="cntm_AdjustmentsToAdditionalPaidInCapitalChangeInMinorityOwnershipInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AdjustmentsToAdditionalPaidInCapitalChangeInMinorityOwnershipInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase (decrease) in additional paid-in capital (APIC) resulting from change in minority ownership percentage.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AdjustmentsToAdditionalPaidInCapitalChangeInMinorityOwnershipInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments to Additional Paid in Capital, Change in Minority Ownership Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AdjustmentsToAdditionalPaidInCapitalChangeInMinorityOwnershipInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition of additional noncontrolling shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender" xlink:to="cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity impact of the value of new stock issued during the period in connection with extinguish obligations to vendors and lenders.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Issued For Extinguish Obligations To Vendors And Lender</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to extinguish obligations to vendors and lenders under 3a10 plan</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForExtinguishObligationsToVendorsAndLender_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate fair value</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders" xlink:to="cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of new stock issued during the period in connection with extinguish obligations to vendors and lenders.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Issued For Extinguish Obligations To Vendors And Lenders</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to extinguish obligations to vendors and lenders under 3a10 plan (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForExtinguishObligationsToVendorsAndLenders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueIssuedForServices" xlink:label="us-gaap_StockIssuedDuringPeriodValueIssuedForServices" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueIssuedForServices" xlink:to="us-gaap_StockIssuedDuringPeriodValueIssuedForServices_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodValueIssuedForServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Issued for Services</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodValueIssuedForServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to vendors as consideration</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:label="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:to="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Issued for Services</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to vendors as consideration (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued as a consideration for commitment fee (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ShareIssuedDuringPeriodValueSettlementForAdvisoryServices" xlink:label="cntm_ShareIssuedDuringPeriodValueSettlementForAdvisoryServices" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ShareIssuedDuringPeriodValueSettlementForAdvisoryServices" xlink:to="cntm_ShareIssuedDuringPeriodValueSettlementForAdvisoryServices_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ShareIssuedDuringPeriodValueSettlementForAdvisoryServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued in connection settlement for services provided by advisory service provider.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ShareIssuedDuringPeriodValueSettlementForAdvisoryServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Issued During Period, Value, Settlement For Advisory Services</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ShareIssuedDuringPeriodValueSettlementForAdvisoryServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to extinguish note payable, related party</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ShareIssuedDuringPeriodSharesSettlementForAdvisoryServices" xlink:label="cntm_ShareIssuedDuringPeriodSharesSettlementForAdvisoryServices" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ShareIssuedDuringPeriodSharesSettlementForAdvisoryServices" xlink:to="cntm_ShareIssuedDuringPeriodSharesSettlementForAdvisoryServices_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ShareIssuedDuringPeriodSharesSettlementForAdvisoryServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued in connection settlement for services provided by advisory service provider.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ShareIssuedDuringPeriodSharesSettlementForAdvisoryServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Issued During Period, Shares, Settlement For Advisory Services</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ShareIssuedDuringPeriodSharesSettlementForAdvisoryServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to extinguish note payable, related party (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement" xlink:label="cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement" xlink:to="cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity impact of the value of new stock issued during the period pursuant to standby equity purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Standby Equity Purchase Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with the conversion of SEPA convertible debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueStandbyEquityPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock for Standby Equity Purchase Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodSharesStandbyEquityPurchaseAgreement" xlink:label="cntm_StockIssuedDuringPeriodSharesStandbyEquityPurchaseAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesStandbyEquityPurchaseAgreement" xlink:to="cntm_StockIssuedDuringPeriodSharesStandbyEquityPurchaseAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesStandbyEquityPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of new stock issued during the period pursuant to standby equity purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesStandbyEquityPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Standby Equity Purchase Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesStandbyEquityPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with the conversion of SEPA convertible debt (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesStandbyEquityPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock for Standby Equity Purchase Agreement (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodValueIssuedForStockSubscription" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForStockSubscription" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueIssuedForStockSubscription" xlink:to="cntm_StockIssuedDuringPeriodValueIssuedForStockSubscription_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForStockSubscription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity impact of the value of new stock issued during the period in connection with stock subscription.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForStockSubscription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Issued For Stock Subscription</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedForStockSubscription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with stock subscription</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodSharesIssuedForStockSubscription" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForStockSubscription" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesIssuedForStockSubscription" xlink:to="cntm_StockIssuedDuringPeriodSharesIssuedForStockSubscription_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForStockSubscription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of new stock issued during the period in connection with stock subscription.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForStockSubscription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Issued For Stock Subscription</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedForStockSubscription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with stock subscription (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share based compensation expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:label="us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:to="us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Conversion of Convertible Securities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion of convertible debt and accrued interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with the conversion of convertible debt and accrued interest 3a9</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:to="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Conversion of Convertible Securities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion of convertible debt and accrued interest (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with the conversion of convertible debt and accrued interest 3a9 (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodValueSettlementOfAccountsPayableVendors" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementOfAccountsPayableVendors" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueSettlementOfAccountsPayableVendors" xlink:to="cntm_StockIssuedDuringPeriodValueSettlementOfAccountsPayableVendors_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementOfAccountsPayableVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of shares issued for settlement of vendors obligation classified in accounts payable.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementOfAccountsPayableVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Settlement Of Accounts Payable Vendors</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueSettlementOfAccountsPayableVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with share exchange agreement to settled accounts payable vendors</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodSharesSettlementOfAccountsPayableVendors" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementOfAccountsPayableVendors" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesSettlementOfAccountsPayableVendors" xlink:to="cntm_StockIssuedDuringPeriodSharesSettlementOfAccountsPayableVendors_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementOfAccountsPayableVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued for settlement of vendors obligation classified in accounts payable.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementOfAccountsPayableVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Settlement Of Accounts Payable Vendors</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesSettlementOfAccountsPayableVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with share exchange agreement to settled accounts payable vendors (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodValueIssuedToBoardOfDirectorsAndEmployees" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedToBoardOfDirectorsAndEmployees" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueIssuedToBoardOfDirectorsAndEmployees" xlink:to="cntm_StockIssuedDuringPeriodValueIssuedToBoardOfDirectorsAndEmployees_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedToBoardOfDirectorsAndEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity impact of the value of new stock issued during the period to board of directors and employees.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedToBoardOfDirectorsAndEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Issued To Board Of Directors And Employees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueIssuedToBoardOfDirectorsAndEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to BOD and employees</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodSharesIssuedToBoardOfDirectorsAndEmployees" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedToBoardOfDirectorsAndEmployees" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesIssuedToBoardOfDirectorsAndEmployees" xlink:to="cntm_StockIssuedDuringPeriodSharesIssuedToBoardOfDirectorsAndEmployees_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedToBoardOfDirectorsAndEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of new stock issued during the period to board of directors and employees.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedToBoardOfDirectorsAndEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Issued To Board Of Directors And Employees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedToBoardOfDirectorsAndEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock to BOD and employees (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodValueEquityMethodInvestment" xlink:label="cntm_StockIssuedDuringPeriodValueEquityMethodInvestment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodValueEquityMethodInvestment" xlink:to="cntm_StockIssuedDuringPeriodValueEquityMethodInvestment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodValueEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of stock issued pursuant to an equity method investment entered during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodValueEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Equity Method Investment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodValueEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with equity method investment in Sun Solar</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_IssuanceOfCommonStockInConnectionWithEquityMethodInvestmentInSunSolar" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithEquityMethodInvestmentInSunSolar" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IssuanceOfCommonStockInConnectionWithEquityMethodInvestmentInSunSolar" xlink:to="cntm_IssuanceOfCommonStockInConnectionWithEquityMethodInvestmentInSunSolar_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithEquityMethodInvestmentInSunSolar_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of stock issued during the period pursuant to an equity method investment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithEquityMethodInvestmentInSunSolar_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with equity method investment in Sun Solar</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithEquityMethodInvestmentInSunSolar_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with equity method investment in Sun Solar (in shares)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodSharesAdjustmentsDueToReverseStockSplits" xlink:label="cntm_StockIssuedDuringPeriodSharesAdjustmentsDueToReverseStockSplits" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesAdjustmentsDueToReverseStockSplits" xlink:to="cntm_StockIssuedDuringPeriodSharesAdjustmentsDueToReverseStockSplits_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesAdjustmentsDueToReverseStockSplits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments to the number of shares during the period as a result of a reverse stock split.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesAdjustmentsDueToReverseStockSplits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Adjustments Due to Reverse Stock Splits</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesAdjustmentsDueToReverseStockSplits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fractional share adjustment due to reverse stock split (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xlink:label="us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xlink:to="us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Income (Loss), Including Portion Attributable to Nonredeemable Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfCashFlowsAbstract" xlink:label="us-gaap_StatementOfCashFlowsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfCashFlowsAbstract" xlink:to="us-gaap_StatementOfCashFlowsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Operating Activities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CASH FLOWS FROM OPERATING ACTIVITIES:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments to reconcile net loss to net cash used in operating activities:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepreciationDepletionAndAmortization" xlink:label="us-gaap_DepreciationDepletionAndAmortization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DepreciationDepletionAndAmortization" xlink:to="us-gaap_DepreciationDepletionAndAmortization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation, Depletion and Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation and amortization expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfDebtDiscountPremium" xlink:label="us-gaap_AmortizationOfDebtDiscountPremium" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AmortizationOfDebtDiscountPremium" xlink:to="us-gaap_AmortizationOfDebtDiscountPremium_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AmortizationOfDebtDiscountPremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of Debt Discount (Premium)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AmortizationOfDebtDiscountPremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of debt discount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensation" xlink:label="us-gaap_ShareBasedCompensation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensation" xlink:to="us-gaap_ShareBasedCompensation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Noncash Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock-based compensation expense</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SharesIssuedForPaymentOfService" xlink:label="cntm_SharesIssuedForPaymentOfService" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SharesIssuedForPaymentOfService" xlink:to="cntm_SharesIssuedForPaymentOfService_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SharesIssuedForPaymentOfService_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of shares issued for payment of service in operating activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SharesIssuedForPaymentOfService_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares Issued For Payment Of Service</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SharesIssuedForPaymentOfService_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares issue for service</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SharesIssuedForPaymentOfSepaConvertibleNoteOfUpfrontFees" xlink:label="cntm_SharesIssuedForPaymentOfSepaConvertibleNoteOfUpfrontFees" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SharesIssuedForPaymentOfSepaConvertibleNoteOfUpfrontFees" xlink:to="cntm_SharesIssuedForPaymentOfSepaConvertibleNoteOfUpfrontFees_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SharesIssuedForPaymentOfSepaConvertibleNoteOfUpfrontFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of shares issued for payment of SEPA convertible note of upfront fees in operating activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SharesIssuedForPaymentOfSepaConvertibleNoteOfUpfrontFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares Issued For Payment Of SEPA Convertible Note Of Upfront Fees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SharesIssuedForPaymentOfSepaConvertibleNoteOfUpfrontFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share issued for SEPA</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SharesIssuedForPaymentOfSettlementOfExpenses" xlink:label="cntm_SharesIssuedForPaymentOfSettlementOfExpenses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SharesIssuedForPaymentOfSettlementOfExpenses" xlink:to="cntm_SharesIssuedForPaymentOfSettlementOfExpenses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SharesIssuedForPaymentOfSettlementOfExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of shares issued for payment of settlement of expenses in operating activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SharesIssuedForPaymentOfSettlementOfExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares Issued For Payment Of Settlement Of Expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SharesIssuedForPaymentOfSettlementOfExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share issues for settlement of expense</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockbasedCompensationToEmployees" xlink:label="cntm_StockbasedCompensationToEmployees" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockbasedCompensationToEmployees" xlink:to="cntm_StockbasedCompensationToEmployees_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockbasedCompensationToEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of stock-based compensation to employees in operating activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockbasedCompensationToEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockbased Compensation To Employees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockbasedCompensationToEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock-based compensation to employees</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAmortization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:to="us-gaap_FinanceLeaseRightOfUseAssetAmortization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Right-of-Use Asset, Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ROU amortization on finance leases</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of ROU assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:to="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Right-of-Use Asset, Periodic Reduction</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ROU amortization on operating leases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentOtherThanTemporaryImpairment" xlink:label="us-gaap_EquityMethodInvestmentOtherThanTemporaryImpairment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentOtherThanTemporaryImpairment" xlink:to="us-gaap_EquityMethodInvestmentOtherThanTemporaryImpairment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentOtherThanTemporaryImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Other-than-Temporary Impairment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentOtherThanTemporaryImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bad debt expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EquityMethodInvestmentOtherThanTemporaryImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment write off</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProvisionForDoubtfulAccounts" xlink:label="us-gaap_ProvisionForDoubtfulAccounts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProvisionForDoubtfulAccounts" xlink:to="us-gaap_ProvisionForDoubtfulAccounts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Credit Loss Expense (Reversal)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Provision for credit losses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Provision for credit losses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryWriteDown" xlink:label="us-gaap_InventoryWriteDown" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryWriteDown" xlink:to="us-gaap_InventoryWriteDown_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryWriteDown_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory Write-down</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryWriteDown_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reduction in carrying value of inventories</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_InventoryWriteDown_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Provision for inventory shrinkage</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:to="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Disposition of Property Plant Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on disposal of property and equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on disposal</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LossOnExtinguishmentOfDebtAndVendorPayable" xlink:label="cntm_LossOnExtinguishmentOfDebtAndVendorPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LossOnExtinguishmentOfDebtAndVendorPayable" xlink:to="cntm_LossOnExtinguishmentOfDebtAndVendorPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LossOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the loss recognized in earnings upon settlement, extinguishment, or restructuring of outstanding debt obligations and trade/vendor payables, including transactions where such obligations are settled through issuance of equity instruments or other non-cash consideration. The loss is measured as the excess of the consideration transferred (including the fair value of equity instruments issued) over the carrying amount of the liabilities extinguished.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LossOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on Extinguishment of Debt and Vendor Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LossOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on extinguishment of debt and vendor payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GainOnExtinguishmentOfDebtAndVendorPayable" xlink:label="cntm_GainOnExtinguishmentOfDebtAndVendorPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GainOnExtinguishmentOfDebtAndVendorPayable" xlink:to="cntm_GainOnExtinguishmentOfDebtAndVendorPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GainOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain recognized gain on extinguishment of debt and vendor payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GainOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain On Extinguishment of Debt And Vendor Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_GainOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on extinguishment of debt and vendor payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt" xlink:label="cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt" xlink:to="cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain (loss) increase (decrease) on change in fair value of convertible debt during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase Decrease In Gain (Loss) On Fair Value Measurement Of Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of convertible debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreementPutOptionLiability" xlink:label="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreementPutOptionLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreementPutOptionLiability" xlink:to="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreementPutOptionLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreementPutOptionLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The net change in the difference between the fair value and the carrying value, or in the comparative fair values, of forward purchase agreement put option liabilities, held at each balance sheet date, that was included in earnings for the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreementPutOptionLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrealized Gain (Loss) on Derivatives, Liabilities, Forward Purchase Agreement, Put Option Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreementPutOptionLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of forward purchase agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_UnrealizedGainLossOnDerivativesLiabilitiesForwardPurchaseAgreementPutOptionLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of forward purchase agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LossOfAcquisitionOfSubsidiary" xlink:label="cntm_LossOfAcquisitionOfSubsidiary" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LossOfAcquisitionOfSubsidiary" xlink:to="cntm_LossOfAcquisitionOfSubsidiary_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LossOfAcquisitionOfSubsidiary_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of loss incurred on acquisition of subsidiary during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LossOfAcquisitionOfSubsidiary_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss Of Acquisition Of Subsidiary</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LossOfAcquisitionOfSubsidiary_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on reposessed vehicle</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnTerminationOfLease" xlink:label="us-gaap_GainLossOnTerminationOfLease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnTerminationOfLease" xlink:to="us-gaap_GainLossOnTerminationOfLease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainLossOnTerminationOfLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Termination of Lease</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_GainLossOnTerminationOfLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on termination of lease</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_IncomeFromSaleOfPropertyAndEquipment" xlink:label="cntm_IncomeFromSaleOfPropertyAndEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IncomeFromSaleOfPropertyAndEquipment" xlink:to="cntm_IncomeFromSaleOfPropertyAndEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IncomeFromSaleOfPropertyAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of Income from sale of property and equipment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IncomeFromSaleOfPropertyAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income from sale of property and equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_IncomeFromSaleOfPropertyAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income from sale of property and equipment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GainLossesOnInitialRecognitionOfDebtAndConvertibleNotes" xlink:label="cntm_GainLossesOnInitialRecognitionOfDebtAndConvertibleNotes" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GainLossesOnInitialRecognitionOfDebtAndConvertibleNotes" xlink:to="cntm_GainLossesOnInitialRecognitionOfDebtAndConvertibleNotes_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GainLossesOnInitialRecognitionOfDebtAndConvertibleNotes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of gain (loss) on initial recognition of debt instruments including convertible notes by the entity during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GainLossesOnInitialRecognitionOfDebtAndConvertibleNotes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Losses) On Initial Recognition Of Debt And Convertible Notes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_GainLossesOnInitialRecognitionOfDebtAndConvertibleNotes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Day one gain on issuance of SEPA and convertible note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GainOnForwardPurchaseAgreementModification" xlink:label="cntm_GainOnForwardPurchaseAgreementModification" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GainOnForwardPurchaseAgreementModification" xlink:to="cntm_GainOnForwardPurchaseAgreementModification_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GainOnForwardPurchaseAgreementModification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain on modifications to forward purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GainOnForwardPurchaseAgreementModification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain On Forward Purchase Agreement Modification</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_GainOnForwardPurchaseAgreementModification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on modification of forward purchase agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ReleasesOfRecycledSharesRelatedToForwardPurchaseAgreementModification" xlink:label="cntm_ReleasesOfRecycledSharesRelatedToForwardPurchaseAgreementModification" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ReleasesOfRecycledSharesRelatedToForwardPurchaseAgreementModification" xlink:to="cntm_ReleasesOfRecycledSharesRelatedToForwardPurchaseAgreementModification_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ReleasesOfRecycledSharesRelatedToForwardPurchaseAgreementModification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of recycled shares released as consideration related to modification on forward purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ReleasesOfRecycledSharesRelatedToForwardPurchaseAgreementModification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Releases Of Recycled Shares Related To Forward Purchase Agreement Modification</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_ReleasesOfRecycledSharesRelatedToForwardPurchaseAgreementModification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on modification of forward purchase agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LossOnForwardPurchaseAgreementModification" xlink:label="cntm_LossOnForwardPurchaseAgreementModification" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LossOnForwardPurchaseAgreementModification" xlink:to="cntm_LossOnForwardPurchaseAgreementModification_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LossOnForwardPurchaseAgreementModification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of recycled shares released as consideration related to modification on forward purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LossOnForwardPurchaseAgreementModification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss On Forward Purchase Agreement Modification</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_LossOnForwardPurchaseAgreementModification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on modification of forward purchase agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainsLossesOnRestructuringOfDebt" xlink:label="us-gaap_GainsLossesOnRestructuringOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainsLossesOnRestructuringOfDebt" xlink:to="us-gaap_GainsLossesOnRestructuringOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainsLossesOnRestructuringOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gains (Losses) on Restructuring of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_GainsLossesOnRestructuringOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on modification of liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GainsLossesOnRestructuringOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (loss) on debt modification</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Operating Capital [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Changes in operating assets and liabilities:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Accounts Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:to="us-gaap_IncreaseDecreaseInContractWithCustomerAsset_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Contract with Customer, Asset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract asset</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherReceivables" xlink:label="us-gaap_IncreaseDecreaseInOtherReceivables" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOtherReceivables" xlink:to="us-gaap_IncreaseDecreaseInOtherReceivables_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOtherReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Other Receivables</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInOtherReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInInventories" xlink:label="us-gaap_IncreaseDecreaseInInventories" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInInventories" xlink:to="us-gaap_IncreaseDecreaseInInventories_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Inventories</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:to="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Prepaid Expense and Other Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepaid expenses and other current assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:label="us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:to="us-gaap_IncreaseDecreaseInOtherNoncurrentAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOtherNoncurrentAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Other Noncurrent Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInOtherNoncurrentAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccountsPayable" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsPayable" xlink:to="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Accounts Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:to="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Accrued Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:to="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Operating Lease Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_IncreaseDecreaseWorkingCapitalAdvance" xlink:label="cntm_IncreaseDecreaseWorkingCapitalAdvance" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IncreaseDecreaseWorkingCapitalAdvance" xlink:to="cntm_IncreaseDecreaseWorkingCapitalAdvance_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IncreaseDecreaseWorkingCapitalAdvance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase (decrease) working capital advance.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IncreaseDecreaseWorkingCapitalAdvance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) Working Capital Advance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_IncreaseDecreaseWorkingCapitalAdvance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Working capital advances</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_IncreaseDecreaseInContingentLiability" xlink:label="cntm_IncreaseDecreaseInContingentLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IncreaseDecreaseInContingentLiability" xlink:to="cntm_IncreaseDecreaseInContingentLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IncreaseDecreaseInContingentLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase (decrease) in obligation for contingencies.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IncreaseDecreaseInContingentLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Contingent Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_IncreaseDecreaseInContingentLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:to="us-gaap_IncreaseDecreaseInContractWithCustomerLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Contract with Customer, Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Operating Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash used in operating activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Negative cash flow from operating activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash used in operating activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Investing Activities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CASH FLOWS FROM INVESTING ACTIVITIES:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Property, Plant, and Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase of property and equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromDivestitureOfBusinesses" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromDivestitureOfBusinesses" xlink:to="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Divestiture of Businesses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from disposal of GEG</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:label="us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:to="us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Sale of Property, Plant, and Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from the sale of property and equipment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PaymentsForPurchaseOfAdditionalNonControllingInterestInvestingActivities" xlink:label="cntm_PaymentsForPurchaseOfAdditionalNonControllingInterestInvestingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentsForPurchaseOfAdditionalNonControllingInterestInvestingActivities" xlink:to="cntm_PaymentsForPurchaseOfAdditionalNonControllingInterestInvestingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentsForPurchaseOfAdditionalNonControllingInterestInvestingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of cash outflow for additional purchase of non-controlling interest, classified as investing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentsForPurchaseOfAdditionalNonControllingInterestInvestingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments For Purchase Of Additional Non Controlling Interest, Investing Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_PaymentsForPurchaseOfAdditionalNonControllingInterestInvestingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase of additional noncontrolling shares</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAcquiredFromAcquisition" xlink:label="us-gaap_CashAcquiredFromAcquisition" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAcquiredFromAcquisition" xlink:to="us-gaap_CashAcquiredFromAcquisition_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAcquiredFromAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Acquired from Acquisition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAcquiredFromAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash acquired</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToDevelopSoftware" xlink:label="us-gaap_PaymentsToDevelopSoftware" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToDevelopSoftware" xlink:to="us-gaap_PaymentsToDevelopSoftware_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToDevelopSoftware_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Develop Software</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsToDevelopSoftware_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid for capitalized software development costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAcquiredInExcessOfPaymentsToAcquireBusiness" xlink:label="us-gaap_CashAcquiredInExcessOfPaymentsToAcquireBusiness" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAcquiredInExcessOfPaymentsToAcquireBusiness" xlink:to="us-gaap_CashAcquiredInExcessOfPaymentsToAcquireBusiness_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAcquiredInExcessOfPaymentsToAcquireBusiness_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Acquired in Excess of Payments to Acquire Business</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAcquiredInExcessOfPaymentsToAcquireBusiness_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash acquired from acquisition of business, net of purchase price paid</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Investing Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash used in investing activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Financing Activities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CASH FLOWS FROM FINANCING ACTIVITIES:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfDebt" xlink:label="us-gaap_ProceedsFromIssuanceOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfDebt" xlink:to="us-gaap_ProceedsFromIssuanceOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds form the issuance of debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from the issuance of debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromConvertibleDebt" xlink:label="us-gaap_ProceedsFromConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromConvertibleDebt" xlink:to="us-gaap_ProceedsFromConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from convertible debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProceedsFromConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from the issuance of convertible notes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfDebt" xlink:label="us-gaap_RepaymentsOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfDebt" xlink:to="us-gaap_RepaymentsOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash payments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfNotesPayable" xlink:label="us-gaap_RepaymentsOfNotesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfNotesPayable" xlink:to="us-gaap_RepaymentsOfNotesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Notes Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_RepaymentsOfNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments on convertible notes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RepaymentsOfNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of convertible debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProceedsFromFactoringReceivableArrangements" xlink:label="cntm_ProceedsFromFactoringReceivableArrangements" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromFactoringReceivableArrangements" xlink:to="cntm_ProceedsFromFactoringReceivableArrangements_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromFactoringReceivableArrangements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of cash inflows from factoring receivable arrangements.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromFactoringReceivableArrangements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Factoring Receivable Arrangements</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsFromFactoringReceivableArrangements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from factoring receivable arrangements</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PaymentsForFactoringReceivableArrangements" xlink:label="cntm_PaymentsForFactoringReceivableArrangements" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentsForFactoringReceivableArrangements" xlink:to="cntm_PaymentsForFactoringReceivableArrangements_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentsForFactoringReceivableArrangements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of cash outflows from factoring receivable arrangements.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentsForFactoringReceivableArrangements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments for Factoring Receivable Arrangements</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_PaymentsForFactoringReceivableArrangements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of factoring receivable arrangements</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="cntm_PaymentsForFactoringReceivableArrangements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments on factoring receivable arrangements</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PaymentsOfDeferredConsideration" xlink:label="cntm_PaymentsOfDeferredConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentsOfDeferredConsideration" xlink:to="cntm_PaymentsOfDeferredConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentsOfDeferredConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash outflow for repayment of deferred consideration, classified as financing activity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentsOfDeferredConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments Of Deferred Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_PaymentsOfDeferredConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of deferred consideration</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeasePrincipalPayments" xlink:label="us-gaap_FinanceLeasePrincipalPayments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeasePrincipalPayments" xlink:to="us-gaap_FinanceLeasePrincipalPayments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Principal Payments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment on finance leases</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProceedsFromBusinessCombination" xlink:label="cntm_ProceedsFromBusinessCombination" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromBusinessCombination" xlink:to="cntm_ProceedsFromBusinessCombination_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromBusinessCombination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash inflow from business combination, classified as financing activity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromBusinessCombination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Business Combination</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsFromBusinessCombination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from the business combination</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PaymentForReimbursementOfConsiderationSharesOfForwardPurchaseAgreement" xlink:label="cntm_PaymentForReimbursementOfConsiderationSharesOfForwardPurchaseAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentForReimbursementOfConsiderationSharesOfForwardPurchaseAgreement" xlink:to="cntm_PaymentForReimbursementOfConsiderationSharesOfForwardPurchaseAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentForReimbursementOfConsiderationSharesOfForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The cash outflow for the payment for reimbursement of consideration shares pertaining to the forward purchase agreement during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentForReimbursementOfConsiderationSharesOfForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment For Reimbursement Of Consideration Shares Of Forward Purchase Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_PaymentForReimbursementOfConsiderationSharesOfForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment for reimbursement of consideration shares related to Forward Purchase Agreement payment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProceedsFromReimbursementForRecycledSharesOfForwardPurchaseAgreement" xlink:label="cntm_ProceedsFromReimbursementForRecycledSharesOfForwardPurchaseAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromReimbursementForRecycledSharesOfForwardPurchaseAgreement" xlink:to="cntm_ProceedsFromReimbursementForRecycledSharesOfForwardPurchaseAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromReimbursementForRecycledSharesOfForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of cash inflow from the reimbursements for recycled shares of the forward purchase agreement during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromReimbursementForRecycledSharesOfForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Reimbursement For Recycled Shares Of Forward Purchase Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsFromReimbursementForRecycledSharesOfForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reimbursement for Recycled Shares related to Forward Purchase Agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:to="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance of Common Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from issuance of common stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Stock Subscription agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDebtIssuanceCosts" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfDebtIssuanceCosts" xlink:to="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of Debt Issuance Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid for debt issuance costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment of structured fee</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProceedsOfFunds" xlink:label="cntm_ProceedsOfFunds" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsOfFunds" xlink:to="cntm_ProceedsOfFunds_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsOfFunds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of cash inflow from funds.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsOfFunds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds of Funds</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsOfFunds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from premium financing obligations</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_RepaymentOfFunds" xlink:label="cntm_RepaymentOfFunds" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RepaymentOfFunds" xlink:to="cntm_RepaymentOfFunds_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RepaymentOfFunds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of cash outflow from funds.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RepaymentOfFunds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayment of Funds</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_RepaymentOfFunds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayment of premium financing obligations</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProceedsFromCollectionOfAdvanceToLender" xlink:label="cntm_ProceedsFromCollectionOfAdvanceToLender" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromCollectionOfAdvanceToLender" xlink:to="cntm_ProceedsFromCollectionOfAdvanceToLender_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromCollectionOfAdvanceToLender_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The cash inflow from the collection of money previously advanced to a lender.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromCollectionOfAdvanceToLender_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Collection Of Advance To Lender</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsFromCollectionOfAdvanceToLender_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advance from lender</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PaymentsToPredecessor" xlink:label="cntm_PaymentsToPredecessor" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentsToPredecessor" xlink:to="cntm_PaymentsToPredecessor_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentsToPredecessor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The cash outflow associated with payments made to the predecessor.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentsToPredecessor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Predecessor</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_PaymentsToPredecessor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advance to Monterey Capital Acquisition Corporation</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProceedsFromTerminationOfDerivativeInstrument" xlink:label="cntm_ProceedsFromTerminationOfDerivativeInstrument" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromTerminationOfDerivativeInstrument" xlink:to="cntm_ProceedsFromTerminationOfDerivativeInstrument_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromTerminationOfDerivativeInstrument_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The cash inflow from the termination of derivative instrument during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromTerminationOfDerivativeInstrument_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Termination Of Derivative Instrument</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsFromTerminationOfDerivativeInstrument_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Forward Purchase agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Financing Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash provided by financing activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effect of Exchange Rate on Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Continuing Operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effect of exchange rate changes on cash and cash equivalents</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net decrease in cash and cash equivalents</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents, end of the period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents, beginning of the period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplementalCashFlowInformationAbstract" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental Cash Flow Information [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental disclosures of cash flow information:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPaidNet" xlink:label="us-gaap_InterestPaidNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestPaidNet" xlink:to="us-gaap_InterestPaidNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Paid, Excluding Capitalized Interest, Operating Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid for interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxesPaidNet" xlink:label="us-gaap_IncomeTaxesPaidNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxesPaidNet" xlink:to="us-gaap_IncomeTaxesPaidNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Taxes Paid, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid for taxes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:to="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental disclosures of noncash financing information:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:to="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-Use Asset Obtained in Exchange for Operating Lease Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-asset, operating acquired</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DerivativeLiabilityIssuedForExtinguishmentOfLenderAndVendorObligations" xlink:label="cntm_DerivativeLiabilityIssuedForExtinguishmentOfLenderAndVendorObligations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DerivativeLiabilityIssuedForExtinguishmentOfLenderAndVendorObligations" xlink:to="cntm_DerivativeLiabilityIssuedForExtinguishmentOfLenderAndVendorObligations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DerivativeLiabilityIssuedForExtinguishmentOfLenderAndVendorObligations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The value of derivative liability issued related to the entity's obligations to its lenders and vendors.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DerivativeLiabilityIssuedForExtinguishmentOfLenderAndVendorObligations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liability Issued For Extinguishment Of Lender And Vendor Obligations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DerivativeLiabilityIssuedForExtinguishmentOfLenderAndVendorObligations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative liabilities issued in connection with extinguishment of obligations to lenders and vendors through issuance of common stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_IssuanceOfSharesForEquityMethodInvestment" xlink:label="cntm_IssuanceOfSharesForEquityMethodInvestment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IssuanceOfSharesForEquityMethodInvestment" xlink:to="cntm_IssuanceOfSharesForEquityMethodInvestment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IssuanceOfSharesForEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The value of stock issued for equity method investment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IssuanceOfSharesForEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance Of Shares For Equity Method Investment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_IssuanceOfSharesForEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of shares for equity method investment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_IssuanceOfCommitmentSharesInConnectionWithConvertibleDebt" xlink:label="cntm_IssuanceOfCommitmentSharesInConnectionWithConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IssuanceOfCommitmentSharesInConnectionWithConvertibleDebt" xlink:to="cntm_IssuanceOfCommitmentSharesInConnectionWithConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IssuanceOfCommitmentSharesInConnectionWithConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The value of commitment shares issued in connection with convertible debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IssuanceOfCommitmentSharesInConnectionWithConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance Of Commitment Shares In Connection With Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_IssuanceOfCommitmentSharesInConnectionWithConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of commitment shares in connection with convertible debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_IssuanceOfCommonStockInConnectionWithConversionOfSepaConvertibleDebt" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithConversionOfSepaConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IssuanceOfCommonStockInConnectionWithConversionOfSepaConvertibleDebt" xlink:to="cntm_IssuanceOfCommonStockInConnectionWithConversionOfSepaConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithConversionOfSepaConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The value of common stock in connection with the conversion of SEPA convertible debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithConversionOfSepaConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in Connection with the Conversion of SEPA Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_IssuanceOfCommonStockInConnectionWithConversionOfSepaConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock in connection with the conversion of SEPA convertible debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtConversionConvertedInstrumentAmount1" xlink:label="us-gaap_DebtConversionConvertedInstrumentAmount1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtConversionConvertedInstrumentAmount1" xlink:to="us-gaap_DebtConversionConvertedInstrumentAmount1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtConversionConvertedInstrumentAmount1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Conversion, Converted Instrument, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtConversionConvertedInstrumentAmount1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion of convertible debt to common stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConversionOfAdvanceFundingOtherPayableLiabilityIntoConvertibleDebtUponExecutionOfDebtAgreement" xlink:label="cntm_ConversionOfAdvanceFundingOtherPayableLiabilityIntoConvertibleDebtUponExecutionOfDebtAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConversionOfAdvanceFundingOtherPayableLiabilityIntoConvertibleDebtUponExecutionOfDebtAgreement" xlink:to="cntm_ConversionOfAdvanceFundingOtherPayableLiabilityIntoConvertibleDebtUponExecutionOfDebtAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConversionOfAdvanceFundingOtherPayableLiabilityIntoConvertibleDebtUponExecutionOfDebtAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of Conversion of advance funding other payable liability into convertible debt upon execution of debt agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConversionOfAdvanceFundingOtherPayableLiabilityIntoConvertibleDebtUponExecutionOfDebtAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion Of Advance Funding Other Payable Liability Into Convertible Debt Upon Execution Of Debt Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConversionOfAdvanceFundingOtherPayableLiabilityIntoConvertibleDebtUponExecutionOfDebtAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion of advance funding other payable liability into convertible debt upon execution of debt agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationCommonStockIssued" xlink:label="cntm_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationCommonStockIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationCommonStockIssued" xlink:to="cntm_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationCommonStockIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationCommonStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The value of shares issued as [noncash or part noncash] consideration for a business or asset acquired. Noncash is defined as transactions during a period that affect recognized assets or liabilities but that do not result in cash receipts or cash payments in the period. "Part noncash" refers to that portion of the transaction not resulting in cash receipts or cash payments in the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationCommonStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncash or Part Noncash Acquisition, Noncash Financial or Equity Instrument Consideration, Common Stock Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NoncashOrPartNoncashAcquisitionNoncashFinancialOrEquityInstrumentConsiderationCommonStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">common stock issued as consideration to acquire a business</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOfAssetsAcquired" xlink:label="us-gaap_FairValueOfAssetsAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueOfAssetsAcquired" xlink:to="us-gaap_FairValueOfAssetsAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueOfAssetsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value of Assets Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueOfAssetsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vehicles acquired through issuance of debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesReduction" xlink:label="us-gaap_NotesReduction" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesReduction" xlink:to="us-gaap_NotesReduction_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NotesReduction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Reduction</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NotesReduction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt extinguished through repossession of vehicle</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesIssued1" xlink:label="us-gaap_NotesIssued1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesIssued1" xlink:to="us-gaap_NotesIssued1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NotesIssued1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NotesIssued1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vendor obligation exchanged for debt instrument</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_Commonstockissuedforprepaidexpenses" xlink:label="cntm_Commonstockissuedforprepaidexpenses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_Commonstockissuedforprepaidexpenses" xlink:to="cntm_Commonstockissuedforprepaidexpenses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_Commonstockissuedforprepaidexpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of common stock issued for prepaid expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_Commonstockissuedforprepaidexpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CommonStockIssuedForPrepaidExpenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_Commonstockissuedforprepaidexpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock issued for prepaid expenses</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_UnpaidPurchasePriceOfAcquisition" xlink:label="cntm_UnpaidPurchasePriceOfAcquisition" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_UnpaidPurchasePriceOfAcquisition" xlink:to="cntm_UnpaidPurchasePriceOfAcquisition_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_UnpaidPurchasePriceOfAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of unpaid purchase price of acquisition.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_UnpaidPurchasePriceOfAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unpaid Purchase Price Of Acquisition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_UnpaidPurchasePriceOfAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unpaid purchase price of acquisition</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ShareIssuedInConnectionWithDebtConversionAgreements" xlink:label="cntm_ShareIssuedInConnectionWithDebtConversionAgreements" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ShareIssuedInConnectionWithDebtConversionAgreements" xlink:to="cntm_ShareIssuedInConnectionWithDebtConversionAgreements_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ShareIssuedInConnectionWithDebtConversionAgreements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of share issued in connection with debt conversion agreements.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ShareIssuedInConnectionWithDebtConversionAgreements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Issued In Connection With Debt Conversion Agreements</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ShareIssuedInConnectionWithDebtConversionAgreements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares issues in connection with debt conversion agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_RecapitalizationOfNonControllingInterest" xlink:label="cntm_RecapitalizationOfNonControllingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RecapitalizationOfNonControllingInterest" xlink:to="cntm_RecapitalizationOfNonControllingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RecapitalizationOfNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recapitalization amount of non-controlling interest due to change in ownership in a subsidiary.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RecapitalizationOfNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recapitalization Of Non-Controlling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RecapitalizationOfNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recapitalization of noncontrolling interests</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement" xlink:label="cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement" xlink:to="cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The carrying value of accounts payable extinguished with settlement agreement  in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying Value of Accounts Payable Extinguished With Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying value of accounts payable extinguished with 3(a)(10) Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_CarryingValueOfAccountsPayableExtinguishedWithSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable and debt extinguishment through the Section 3(a)(10) Settlement Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CarryingValueOfDebtExtinguished" xlink:label="cntm_CarryingValueOfDebtExtinguished" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CarryingValueOfDebtExtinguished" xlink:to="cntm_CarryingValueOfDebtExtinguished_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CarryingValueOfDebtExtinguished_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The carrying value of debt extinguished in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CarryingValueOfDebtExtinguished_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying Value Of Debt Extinguished</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CarryingValueOfDebtExtinguished_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying value of debt extinguished with 3(a)(10) Settlement Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NonCashInvestingAndFinancingActivitiesFinancedInsurancePremium" xlink:label="cntm_NonCashInvestingAndFinancingActivitiesFinancedInsurancePremium" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NonCashInvestingAndFinancingActivitiesFinancedInsurancePremium" xlink:to="cntm_NonCashInvestingAndFinancingActivitiesFinancedInsurancePremium_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NonCashInvestingAndFinancingActivitiesFinancedInsurancePremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of non cash investing and financing activities financed insurance premium.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NonCashInvestingAndFinancingActivitiesFinancedInsurancePremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non Cash Investing And Financing Activities Financed Insurance Premium</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NonCashInvestingAndFinancingActivitiesFinancedInsurancePremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financed insurance premium in prepaid expense</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ExchangeOfOperatingLeaseLiabilityForAccountsPayableOnTerminatedLease" xlink:label="cntm_ExchangeOfOperatingLeaseLiabilityForAccountsPayableOnTerminatedLease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ExchangeOfOperatingLeaseLiabilityForAccountsPayableOnTerminatedLease" xlink:to="cntm_ExchangeOfOperatingLeaseLiabilityForAccountsPayableOnTerminatedLease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ExchangeOfOperatingLeaseLiabilityForAccountsPayableOnTerminatedLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of non-cash exchange of operating lease liability for accounts payable on terminated lease.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ExchangeOfOperatingLeaseLiabilityForAccountsPayableOnTerminatedLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Exchange of operating lease liability for accounts payable on terminated lease</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DerecognitionOfRightOfUseAssetOperatingOnTerminatedLease" xlink:label="cntm_DerecognitionOfRightOfUseAssetOperatingOnTerminatedLease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DerecognitionOfRightOfUseAssetOperatingOnTerminatedLease" xlink:to="cntm_DerecognitionOfRightOfUseAssetOperatingOnTerminatedLease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DerecognitionOfRightOfUseAssetOperatingOnTerminatedLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of non-cash de-recognition of right-of-use asset, operating on terminated lease.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DerecognitionOfRightOfUseAssetOperatingOnTerminatedLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derecognition of right-of-use asset, operating on terminated lease</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DerecognitionOfRightOfUseAssetOperatingOnTerminatedLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">De-recognition of right of use of asset, operating on terminated lease</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ExtinguishmentOfOperatingLeaseLiabilityOnTerminatedLease" xlink:label="cntm_ExtinguishmentOfOperatingLeaseLiabilityOnTerminatedLease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ExtinguishmentOfOperatingLeaseLiabilityOnTerminatedLease" xlink:to="cntm_ExtinguishmentOfOperatingLeaseLiabilityOnTerminatedLease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ExtinguishmentOfOperatingLeaseLiabilityOnTerminatedLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of non-cash extinguishment of operating lease liability on terminated lease.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ExtinguishmentOfOperatingLeaseLiabilityOnTerminatedLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of operating lease liability on terminated lease</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ExtinguishmentOfOperatingLeaseLiabilityOnTerminatedLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of operating lease liability on terminated lease</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ExtinguishmentOfAccountsPayableThroughIssuanceOfDebt" xlink:label="cntm_ExtinguishmentOfAccountsPayableThroughIssuanceOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ExtinguishmentOfAccountsPayableThroughIssuanceOfDebt" xlink:to="cntm_ExtinguishmentOfAccountsPayableThroughIssuanceOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ExtinguishmentOfAccountsPayableThroughIssuanceOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of extinguishment of accounts payable through issuance of debt in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ExtinguishmentOfAccountsPayableThroughIssuanceOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of Accounts Payable Through Issuance of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ExtinguishmentOfAccountsPayableThroughIssuanceOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of accounts payable through issuance of debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement" xlink:to="cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of shares issued to settle other payables under 3(a)(9) settlement agreement in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value of Shares Issued To Settle Other Payables Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of shares issued to settle Claim under 3(a)(10) Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of shares issued to settle Claim under Section 3(a)(9) Settlement Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueOfSharesIssuedToSettleShareResetDerivativeLiabilities" xlink:label="cntm_FairValueOfSharesIssuedToSettleShareResetDerivativeLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueOfSharesIssuedToSettleShareResetDerivativeLiabilities" xlink:to="cntm_FairValueOfSharesIssuedToSettleShareResetDerivativeLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueOfSharesIssuedToSettleShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of fair value of shares issued to settle share reset derivative liability in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueOfSharesIssuedToSettleShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value of Shares Issued To Settle Share Reset Derivative Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueOfSharesIssuedToSettleShareResetDerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of shares issued to settle the share reset derivative liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of holdback consideration recorded as non-cash investing item.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Including Discontinued Operation, Non-cash Investing items, Holdback</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Holdback recorded as non-cash investing item</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNonCashInvestingItemsHoldback_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration receivable from disposal of GEG</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SettlementOfAccountsPayableThroughIssuanceOfShares" xlink:label="cntm_SettlementOfAccountsPayableThroughIssuanceOfShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementOfAccountsPayableThroughIssuanceOfShares" xlink:to="cntm_SettlementOfAccountsPayableThroughIssuanceOfShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementOfAccountsPayableThroughIssuanceOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of accounts payable settled through issuance of shares in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementOfAccountsPayableThroughIssuanceOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Of Accounts Payable Through Issuance Of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementOfAccountsPayableThroughIssuanceOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement of accounts payable through issuance of shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_RepossessionOfVehicleAmount" xlink:label="cntm_RepossessionOfVehicleAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RepossessionOfVehicleAmount" xlink:to="cntm_RepossessionOfVehicleAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RepossessionOfVehicleAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment due to the repossession of vehicle during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RepossessionOfVehicleAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repossession Of Vehicle, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RepossessionOfVehicleAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repossessed vehicle</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ExtinguishmentOfDerivativeLiability" xlink:label="cntm_ExtinguishmentOfDerivativeLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ExtinguishmentOfDerivativeLiability" xlink:to="cntm_ExtinguishmentOfDerivativeLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ExtinguishmentOfDerivativeLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of extinguishment of derivative liability.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ExtinguishmentOfDerivativeLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment Of Derivative Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ExtinguishmentOfDerivativeLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of derivative liability</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DeRecognitionOfRightOfUseAssetAndLeaseLiability" xlink:label="cntm_DeRecognitionOfRightOfUseAssetAndLeaseLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DeRecognitionOfRightOfUseAssetAndLeaseLiability" xlink:to="cntm_DeRecognitionOfRightOfUseAssetAndLeaseLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DeRecognitionOfRightOfUseAssetAndLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">De-recognition of ROU asset and lease liability on termination of lease.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DeRecognitionOfRightOfUseAssetAndLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">De-Recognition Of Right-Of-Use Asset And Lease Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DeRecognitionOfRightOfUseAssetAndLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Removal of ROU asset and lease liability at lease termination</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ReclassificationOfRemainingObligationUnderTerminatedLease" xlink:label="cntm_ReclassificationOfRemainingObligationUnderTerminatedLease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ReclassificationOfRemainingObligationUnderTerminatedLease" xlink:to="cntm_ReclassificationOfRemainingObligationUnderTerminatedLease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ReclassificationOfRemainingObligationUnderTerminatedLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassification adjustment of remaining obligation under terminated lease.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ReclassificationOfRemainingObligationUnderTerminatedLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassification Of Remaining Obligation Under Terminated Lease</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ReclassificationOfRemainingObligationUnderTerminatedLease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassification of remaining obligation under terminated lease</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueOfSharesIssuedToSettleOtherPayablesUnderSettlementAgreement" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesUnderSettlementAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueOfSharesIssuedToSettleOtherPayablesUnderSettlementAgreement" xlink:to="cntm_FairValueOfSharesIssuedToSettleOtherPayablesUnderSettlementAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesUnderSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of fair value of shares issued to settle other payables under settlement agreement in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesUnderSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value of Shares Issued To Settle Other Payables Under Settlement Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueOfSharesIssuedToSettleOtherPayablesUnderSettlementAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of shares issued to settle Claim under Section 3(a)(10) Settlement Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueOfSharesIssuedOnConversionOfSepaConvertibleDebt" xlink:label="cntm_FairValueOfSharesIssuedOnConversionOfSepaConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueOfSharesIssuedOnConversionOfSepaConvertibleDebt" xlink:to="cntm_FairValueOfSharesIssuedOnConversionOfSepaConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueOfSharesIssuedOnConversionOfSepaConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the fair value of equity instruments issued by the entity in connection with the conversion or settlement of convertible debt arrangements under a standby equity purchase agreement (SEPA). The amount reflects the fair value of shares issued at the conversion date and is used in determining the gain or loss on extinguishment of the related debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueOfSharesIssuedOnConversionOfSepaConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value of Shares Issued on Conversion of SEPA Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueOfSharesIssuedOnConversionOfSepaConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of shares in connection with the conversion of SEPA convertible debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SharesIssuedToVendorForPrepaidExpensesAndAccountsPayable" xlink:label="cntm_SharesIssuedToVendorForPrepaidExpensesAndAccountsPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SharesIssuedToVendorForPrepaidExpensesAndAccountsPayable" xlink:to="cntm_SharesIssuedToVendorForPrepaidExpensesAndAccountsPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SharesIssuedToVendorForPrepaidExpensesAndAccountsPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of shares issued to vendor for prepaid expenses and accounts payable in non-cash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SharesIssuedToVendorForPrepaidExpensesAndAccountsPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares Issued To Vendor For Prepaid Expenses And Accounts Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SharesIssuedToVendorForPrepaidExpensesAndAccountsPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares issued to vendor for prepaid expenses and accounts payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessOnStockIssued" xlink:label="cntm_BusinessOnStockIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessOnStockIssued" xlink:to="cntm_BusinessOnStockIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessOnStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The stock issued in noncash financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessOnStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business on stock issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessOnStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share issues</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AcquisitionOfNonControllingInterest" xlink:label="cntm_AcquisitionOfNonControllingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AcquisitionOfNonControllingInterest" xlink:to="cntm_AcquisitionOfNonControllingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AcquisitionOfNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase in non-controlling interest during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AcquisitionOfNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition Of Non-Controlling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_AcquisitionOfNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition of proprietary technology</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PromissoryNoteInConnectionWithGeoImpexAcquisition" xlink:label="cntm_PromissoryNoteInConnectionWithGeoImpexAcquisition" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PromissoryNoteInConnectionWithGeoImpexAcquisition" xlink:to="cntm_PromissoryNoteInConnectionWithGeoImpexAcquisition_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PromissoryNoteInConnectionWithGeoImpexAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of modification of promissory note in connection with Geo Impex acquisition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PromissoryNoteInConnectionWithGeoImpexAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Promissory note in connection with Geo Impex acquisition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_PromissoryNoteInConnectionWithGeoImpexAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Promissory note in connection with Geo Impex acquisition</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ExtinguishmentOfDerivativeLiabilityThroughDebtObligation" xlink:label="cntm_ExtinguishmentOfDerivativeLiabilityThroughDebtObligation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ExtinguishmentOfDerivativeLiabilityThroughDebtObligation" xlink:to="cntm_ExtinguishmentOfDerivativeLiabilityThroughDebtObligation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ExtinguishmentOfDerivativeLiabilityThroughDebtObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of extinguishment of derivative liability through the recognition of a reinstated debt obligation amounting.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ExtinguishmentOfDerivativeLiabilityThroughDebtObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment Of Derivative Liability Through Debt Obligation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ExtinguishmentOfDerivativeLiabilityThroughDebtObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of derivative liability through the recognition of a reinstated debt obligation amounting</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ORGANIZATION AND OPERATIONS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NatureOfOperations" xlink:label="us-gaap_NatureOfOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NatureOfOperations" xlink:to="us-gaap_NatureOfOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NatureOfOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nature of Operations [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NatureOfOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ORGANIZATION AND OPERATIONS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract" xlink:label="us-gaap_AccountingPoliciesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_AccountingPoliciesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountingPoliciesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SignificantAccountingPoliciesTextBlock" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Significant Accounting Policies [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GoingConcernAbstract" xlink:label="cntm_GoingConcernAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GoingConcernAbstract" xlink:to="cntm_GoingConcernAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GoingConcernAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">No definition available.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GoingConcernAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">GOING CONCERN</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubstantialDoubtAboutGoingConcernTextBlock" xlink:label="us-gaap_SubstantialDoubtAboutGoingConcernTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubstantialDoubtAboutGoingConcernTextBlock" xlink:to="us-gaap_SubstantialDoubtAboutGoingConcernTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubstantialDoubtAboutGoingConcernTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Substantial Doubt about Going Concern [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubstantialDoubtAboutGoingConcernTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">GOING CONCERN</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:label="us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:to="us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DISPOSALS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:to="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Groups, Including Discontinued Operations, Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DISPOSALS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:label="us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:to="us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">INVESTMENT IN SUN SOLAR - EQUITY METHOD</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:label="us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:to="us-gaap_EquityMethodInvestmentsDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investments and Joint Ventures Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">INVESTMENT IN SUN SOLAR - EQUITY METHOD</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:to="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">INTANGIBLE ASSETS, NET</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:label="us-gaap_IntangibleAssetsDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:to="us-gaap_IntangibleAssetsDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IntangibleAssetsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Assets Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IntangibleAssetsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">INTANGIBLE ASSETS, NET</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermConvertibleDebtCurrentAndNoncurrentAbstract" xlink:label="us-gaap_LongtermConvertibleDebtCurrentAndNoncurrentAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongtermConvertibleDebtCurrentAndNoncurrentAbstract" xlink:to="us-gaap_LongtermConvertibleDebtCurrentAndNoncurrentAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongtermConvertibleDebtCurrentAndNoncurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CONVERTIBLE DEBT</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleDebtTextBlock" xlink:label="cntm_ConvertibleDebtTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleDebtTextBlock" xlink:to="cntm_ConvertibleDebtTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleDebtTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The entire disclosure of the entity's convertible debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleDebtTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Debt [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleDebtTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CONVERTIBLE DEBT</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtDisclosureAbstract" xlink:label="us-gaap_DebtDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtDisclosureAbstract" xlink:to="us-gaap_DebtDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DEBT</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtDisclosureTextBlock" xlink:label="us-gaap_DebtDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtDisclosureTextBlock" xlink:to="us-gaap_DebtDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DEBT</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract" xlink:label="us-gaap_FairValueDisclosuresAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueDisclosuresAbstract" xlink:to="us-gaap_FairValueDisclosuresAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueDisclosuresAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">FAIR VALUE MEASUREMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresTextBlock" xlink:label="us-gaap_FairValueDisclosuresTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueDisclosuresTextBlock" xlink:to="us-gaap_FairValueDisclosuresTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Disclosures [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">FAIR VALUE MEASUREMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsAbstract" xlink:label="us-gaap_RelatedPartyTransactionsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">RELATED PARTY TRANSACTIONS</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:label="us-gaap_RevenueFromContractWithCustomerTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureTextBlock" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingAbstract" xlink:label="us-gaap_SegmentReportingAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingAbstract" xlink:to="us-gaap_SegmentReportingAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REPORTABLE SEGMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingDisclosureTextBlock" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment Reporting Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REPORTABLE SEGMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsAbstract" xlink:label="us-gaap_SubsequentEventsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SUBSEQUENT EVENTS</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Events [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SUBSEQUENT EVENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock" xlink:label="us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:label="us-gaap_SegmentReportingPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment Reporting, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentReportingPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment reporting</label>
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    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NonControllingInterestPolicyTextBlock" xlink:label="cntm_NonControllingInterestPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComparabilityOfPriorYearFinancialData" xlink:label="us-gaap_ComparabilityOfPriorYearFinancialData" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComparabilityOfPriorYearFinancialData" xlink:to="us-gaap_ComparabilityOfPriorYearFinancialData_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComparabilityOfPriorYearFinancialData_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comparability of Prior Year Financial Data, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ComparabilityOfPriorYearFinancialData_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounting Treatment and Retroactive Restatement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basis of Accounting, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Significant Accounting Policies</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:label="us-gaap_PriorPeriodReclassificationAdjustmentDescription" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:to="us-gaap_PriorPeriodReclassificationAdjustmentDescription_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PriorPeriodReclassificationAdjustmentDescription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassification, Comparability Adjustment [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PriorPeriodReclassificationAdjustmentDescription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassifications</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">New Accounting Pronouncements, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recently issued accounting pronouncements, adopted and not yet adopted</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EmergingGrowthCompanyPolicyTextBlock" xlink:label="cntm_EmergingGrowthCompanyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EmergingGrowthCompanyPolicyTextBlock" xlink:to="cntm_EmergingGrowthCompanyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EmergingGrowthCompanyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy on Emerging Growth Company.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EmergingGrowthCompanyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Emerging Growth Company [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EmergingGrowthCompanyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Emerging growth company</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and Cash Equivalents, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:label="us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:to="us-gaap_FairValueMeasurementPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Measurement, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueMeasurementPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value measurements</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_RelatedPartiesPolicyPolicyTextBlock" xlink:label="cntm_RelatedPartiesPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RelatedPartiesPolicyPolicyTextBlock" xlink:to="cntm_RelatedPartiesPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RelatedPartiesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for related parties.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RelatedPartiesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Parties, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RelatedPartiesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related parties</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivablesPolicyTextBlock" xlink:label="us-gaap_ReceivablesPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ReceivablesPolicyTextBlock" xlink:to="us-gaap_ReceivablesPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ReceivablesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Receivable [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ReceivablesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable and allowance for credit losses</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotesReceivableRelatedPartyPolicyPolicyTextBlock" xlink:label="cntm_ConvertibleNotesReceivableRelatedPartyPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotesReceivableRelatedPartyPolicyPolicyTextBlock" xlink:to="cntm_ConvertibleNotesReceivableRelatedPartyPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotesReceivableRelatedPartyPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for convertible notes receivable relating to related parties.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotesReceivableRelatedPartyPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes Receivable, Related Party, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotesReceivableRelatedPartyPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible notes receivable, related party</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PrepaidExpensesAndOtherCurrentAssetsPolicyPolicyTextBlock" xlink:label="cntm_PrepaidExpensesAndOtherCurrentAssetsPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PrepaidExpensesAndOtherCurrentAssetsPolicyPolicyTextBlock" xlink:to="cntm_PrepaidExpensesAndOtherCurrentAssetsPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PrepaidExpensesAndOtherCurrentAssetsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy prepaid expenses and other current assets.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PrepaidExpensesAndOtherCurrentAssetsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepaid Expenses And Other Current Assets, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PrepaidExpensesAndOtherCurrentAssetsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepaid expenses and other current assets</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_WorkingCapitalAdvancesToManagedSegmentCustomersPolicyPolicyTextBlock" xlink:label="cntm_WorkingCapitalAdvancesToManagedSegmentCustomersPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_WorkingCapitalAdvancesToManagedSegmentCustomersPolicyPolicyTextBlock" xlink:to="cntm_WorkingCapitalAdvancesToManagedSegmentCustomersPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_WorkingCapitalAdvancesToManagedSegmentCustomersPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for working capital advances to managed segment customers.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_WorkingCapitalAdvancesToManagedSegmentCustomersPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Working Capital Advances To Managed Segment Customers Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_WorkingCapitalAdvancesToManagedSegmentCustomersPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Working capital advances to managed solutions segment customers</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:to="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property and Equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy" xlink:label="us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy" xlink:to="us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill and Intangible Assets, Intangible Assets, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InternalUseSoftwarePolicy" xlink:label="us-gaap_InternalUseSoftwarePolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InternalUseSoftwarePolicy" xlink:to="us-gaap_InternalUseSoftwarePolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InternalUseSoftwarePolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Internal Use Software, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InternalUseSoftwarePolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Software development costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentPolicyTextBlock" xlink:label="us-gaap_InvestmentPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentPolicyTextBlock" xlink:to="us-gaap_InvestmentPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InvestmentPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InvestmentPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investments in Joint Ventures</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DeferredOfferingCostsPolicyPolicyTextBlock" xlink:label="cntm_DeferredOfferingCostsPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DeferredOfferingCostsPolicyPolicyTextBlock" xlink:to="cntm_DeferredOfferingCostsPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DeferredOfferingCostsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for deferred offering costs.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DeferredOfferingCostsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Offering Costs, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DeferredOfferingCostsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred offering costs</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ImpairmentOrDisposalOfLongLivedAssetsIncludingFiniteLivedIntangibleAssetsPolicyPolicyTextBlock" xlink:label="cntm_ImpairmentOrDisposalOfLongLivedAssetsIncludingFiniteLivedIntangibleAssetsPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ImpairmentOrDisposalOfLongLivedAssetsIncludingFiniteLivedIntangibleAssetsPolicyPolicyTextBlock" xlink:to="cntm_ImpairmentOrDisposalOfLongLivedAssetsIncludingFiniteLivedIntangibleAssetsPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ImpairmentOrDisposalOfLongLivedAssetsIncludingFiniteLivedIntangibleAssetsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for the impairment and disposal of long-lived assets including finite lived intangible assets excluding goodwill.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ImpairmentOrDisposalOfLongLivedAssetsIncludingFiniteLivedIntangibleAssetsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment or Disposal of Long-Lived Assets, Including Finite-Lived Intangible Assets, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ImpairmentOrDisposalOfLongLivedAssetsIncludingFiniteLivedIntangibleAssetsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment of long-lived assets and finite- lived Intangible asset</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:label="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:to="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill and Intangible Assets, Goodwill, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment of Goodwill</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativesPolicyTextBlock" xlink:label="us-gaap_DerivativesPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativesPolicyTextBlock" xlink:to="us-gaap_DerivativesPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivatives, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative financial instruments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NotesPayablePolicyPolicyTextBlock" xlink:label="cntm_NotesPayablePolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NotesPayablePolicyPolicyTextBlock" xlink:to="cntm_NotesPayablePolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NotesPayablePolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for notes payable and notes payable relating to related parties.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NotesPayablePolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payable, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NotesPayablePolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes payable and notes payable - related party</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_NotesPayablePolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes payable and notes payable - related party</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GainLossOnExtinguishmentOfLiabilitiesPolicyPolicyTextBlock" xlink:label="cntm_GainLossOnExtinguishmentOfLiabilitiesPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GainLossOnExtinguishmentOfLiabilitiesPolicyPolicyTextBlock" xlink:to="cntm_GainLossOnExtinguishmentOfLiabilitiesPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GainLossOnExtinguishmentOfLiabilitiesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for gain (loss) on extinguishment of liabilities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GainLossOnExtinguishmentOfLiabilitiesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) On Extinguishment Of Liabilities, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GainLossOnExtinguishmentOfLiabilitiesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gains and losses on extinguishment of liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:label="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:to="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue from Contract with Customer [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue Recognition</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeLeasesPolicyTextBlock" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeLeasesPolicyTextBlock" xlink:to="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Leases [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Leases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostOfSalesPolicyTextBlock" xlink:label="us-gaap_CostOfSalesPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostOfSalesPolicyTextBlock" xlink:to="us-gaap_CostOfSalesPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostOfSalesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cost of Goods and Service [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CostOfSalesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cost of revenues</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SellingGeneralAndAdministrativeExpensesPolicyTextBlock" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpensesPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SellingGeneralAndAdministrativeExpensesPolicyTextBlock" xlink:to="us-gaap_SellingGeneralAndAdministrativeExpensesPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpensesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, General and Administrative Expenses, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpensesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, general and administrative expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdvertisingCostsPolicyTextBlock" xlink:label="us-gaap_AdvertisingCostsPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdvertisingCostsPolicyTextBlock" xlink:to="us-gaap_AdvertisingCostsPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdvertisingCostsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advertising Cost [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdvertisingCostsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advertising expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:label="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:to="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock-based compensation</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_WarrantsPolicyTextBlock" xlink:label="cntm_WarrantsPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_WarrantsPolicyTextBlock" xlink:to="cntm_WarrantsPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_WarrantsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for warrants.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_WarrantsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Warrants [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_WarrantsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Warrants</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:label="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:to="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive loss</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:to="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Foreign Currency Transactions and Translations Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Foreign Currency</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPolicyTextBlock" xlink:label="us-gaap_IncomeTaxPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxPolicyTextBlock" xlink:to="us-gaap_IncomeTaxPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Taxes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:label="us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:to="us-gaap_ScheduleOfInventoryCurrentTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfInventoryCurrentTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Inventories</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ScheduleOfPropertyPlantAndEquipmentUsefulLifeTableTextBlock" xlink:label="cntm_ScheduleOfPropertyPlantAndEquipmentUsefulLifeTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ScheduleOfPropertyPlantAndEquipmentUsefulLifeTableTextBlock" xlink:to="cntm_ScheduleOfPropertyPlantAndEquipmentUsefulLifeTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ScheduleOfPropertyPlantAndEquipmentUsefulLifeTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular disclosure of the useful life of long-lived, physical assets that are used in the normal conduct of business to produce goods and services and not intended for resale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ScheduleOfPropertyPlantAndEquipmentUsefulLifeTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Property, Plant and Equipment, Useful Life [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ScheduleOfPropertyPlantAndEquipmentUsefulLifeTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of property, plant and equipment, useful life</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ScheduleOfFiniteLivedIntangibleAssetsUsefulLifeTableTextBlock" xlink:label="cntm_ScheduleOfFiniteLivedIntangibleAssetsUsefulLifeTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ScheduleOfFiniteLivedIntangibleAssetsUsefulLifeTableTextBlock" xlink:to="cntm_ScheduleOfFiniteLivedIntangibleAssetsUsefulLifeTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ScheduleOfFiniteLivedIntangibleAssetsUsefulLifeTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular disclosure of the useful life of finite lived intangible assets.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ScheduleOfFiniteLivedIntangibleAssetsUsefulLifeTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule Of Finite Lived Intangible Assets Useful Life [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ScheduleOfFiniteLivedIntangibleAssetsUsefulLifeTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of intangible assets, useful life</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:to="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of outstanding shares of common stock equivalents</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ScheduleOfEffectOfReverseStockSplitOnSharesOutstandingTableTextBlock" xlink:label="cntm_ScheduleOfEffectOfReverseStockSplitOnSharesOutstandingTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ScheduleOfEffectOfReverseStockSplitOnSharesOutstandingTableTextBlock" xlink:to="cntm_ScheduleOfEffectOfReverseStockSplitOnSharesOutstandingTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ScheduleOfEffectOfReverseStockSplitOnSharesOutstandingTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular disclosure of effect of reverse stock split on shares outstanding.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ScheduleOfEffectOfReverseStockSplitOnSharesOutstandingTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule Of Effect Of Reverse Stock Split On Shares Outstanding [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ScheduleOfEffectOfReverseStockSplitOnSharesOutstandingTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of reverse stock split</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfGoodwillTextBlock" xlink:label="us-gaap_ScheduleOfGoodwillTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfGoodwillTextBlock" xlink:to="us-gaap_ScheduleOfGoodwillTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfGoodwillTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Goodwill [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfGoodwillTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of changes in carrying amount of goodwill</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related and Nonrelated Parties [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related and Nonrelated Parties [Axis]</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="us-gaap_RelatedPartyDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related and Nonrelated Parties [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonrelatedPartyMember" xlink:label="us-gaap_NonrelatedPartyMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NonrelatedPartyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nonrelated Party [Member]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</label>
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    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2026And2025Member" xlink:label="cntm_ConvertibleNotes2026And2025Member" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026And2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to 2026 and 2025 Convertible Notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026And2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026 and 2025 [Member]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StandbyEquityPurchaseAgreementConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Standby Equity Purchase Agreement Convertible Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StandbyEquityPurchaseAgreementConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SEPA Convertible Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SettlementAgreementMember" xlink:label="cntm_SettlementAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to settlement agreement for shares issued under Section 3(a)(10) of the Securities Act.</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">3(a)(10) Settlement Agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">FAIR VALUE MEASUREMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of assets and liabilities measured and recorded at fair value on a recurring basis</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of reconciliation of assets and liabilities measured at fair value using Level 3 inputs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xlink:label="us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfCarryingValuesAndEstimatedFairValuesOfDebtInstrumentsTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of carrying value and fair value for the convertible notes payable for which the Company elected the fair value option</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Measurement Inputs and Valuation Techniques [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of fair value measurements</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock" xlink:label="us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock" xlink:to="us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue from External Customers by Geographic Areas [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of disaggregated revenue information by geographic area based upon customer's country of domicile</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:label="us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:to="us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Contract Asset, Contract Liability, and Receivable [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of contract assets and liability activity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xlink:label="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xlink:to="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Allowance for Credit Loss [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of accounts receivable and allowance for credit losses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Segment Reporting Information, by Segment [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of reportable segment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:to="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disaggregation of Revenue [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of disaggregated revenue information by geographic area</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_OrganizationAndOperationsTable" xlink:label="cntm_OrganizationAndOperationsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_OrganizationAndOperationsTable" xlink:to="cntm_OrganizationAndOperationsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_OrganizationAndOperationsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of information about organization and operations.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OrganizationAndOperationsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ORGANIZATION AND OPERATIONS [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis" xlink:label="us-gaap_StatementBusinessSegmentsAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementBusinessSegmentsAxis" xlink:to="us-gaap_StatementBusinessSegmentsAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementBusinessSegmentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segments [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain" xlink:label="us-gaap_SegmentDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentDomain" xlink:to="us-gaap_SegmentDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segments [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_KeenLabsSegmentMember" xlink:label="cntm_KeenLabsSegmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_KeenLabsSegmentMember" xlink:to="cntm_KeenLabsSegmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_KeenLabsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Keen Labs' segment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_KeenLabsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Keen Labs Segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_KeenLabsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Keen Labs Operations, Inc</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_KeenLabsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Keen Labs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementGeographicalAxis" xlink:label="srt_StatementGeographicalAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_StatementGeographicalAxis" xlink:to="srt_StatementGeographicalAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_StatementGeographicalAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Geographical [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_SegmentGeographicalDomain" xlink:label="srt_SegmentGeographicalDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_SegmentGeographicalDomain" xlink:to="srt_SegmentGeographicalDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_SegmentGeographicalDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Geographical [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_US" xlink:label="country_US" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="country_US" xlink:to="country_US_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="country_US_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">UNITED STATES</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="country_US_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">United States</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_OrganizationAndOperationsLineItems" xlink:label="cntm_OrganizationAndOperationsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_OrganizationAndOperationsLineItems" xlink:to="cntm_OrganizationAndOperationsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_OrganizationAndOperationsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OrganizationAndOperationsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ORGANIZATION AND OPERATIONS [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_OrganizationAndOperationsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ORGANIZATION AND OPERATIONS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfOperatingSegments" xlink:label="us-gaap_NumberOfOperatingSegments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfOperatingSegments" xlink:to="us-gaap_NumberOfOperatingSegments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Operating Segments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of operating segments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SummaryOfSignificantAccountingPoliciesTable" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SummaryOfSignificantAccountingPoliciesTable" xlink:to="cntm_SummaryOfSignificantAccountingPoliciesTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule reflecting a summary of significant accounting policies.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Summary of Significant Accounting Policies [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis" xlink:label="srt_RangeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeAxis" xlink:to="srt_RangeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RangeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statistical Measurement [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember" xlink:label="srt_RangeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeMember" xlink:to="srt_RangeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RangeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statistical Measurement [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember" xlink:label="srt_MinimumMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MinimumMember" xlink:to="srt_MinimumMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MinimumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_MinimumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember" xlink:label="srt_MaximumMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MaximumMember" xlink:to="srt_MaximumMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MaximumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_MaximumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateMember" xlink:label="us-gaap_CorporateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CorporateMember" xlink:to="us-gaap_CorporateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CorporateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Corporate Segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CorporateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Corporate, Defense and Strategic Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CorporateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Corporate and Strategic Assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonUsMember" xlink:label="us-gaap_NonUsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NonUsMember" xlink:to="us-gaap_NonUsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NonUsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-US [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NonUsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_IN" xlink:label="country_IN" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="country_IN" xlink:to="country_IN_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="country_IN_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">INDIA</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="country_IN_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">India</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="country_IN_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chhatrapur, Odisha, India</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SummaryOfSignificantAccountingPoliciesLineItems" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SummaryOfSignificantAccountingPoliciesLineItems" xlink:to="cntm_SummaryOfSignificantAccountingPoliciesLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Summary of Significant Accounting Policies [Line Items}</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_SummaryOfSignificantAccountingPoliciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfReportableSegments" xlink:label="us-gaap_NumberOfReportableSegments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfReportableSegments" xlink:to="us-gaap_NumberOfReportableSegments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Reportable Segments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of reportable segments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AreaOfLand" xlink:label="us-gaap_AreaOfLand" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AreaOfLand" xlink:to="us-gaap_AreaOfLand_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AreaOfLand_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Area of Land</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AreaOfLand_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Area of land</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_UnrealizedGainLossOnFairValueMeasurementOfConvertibleDebt" xlink:label="cntm_UnrealizedGainLossOnFairValueMeasurementOfConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_UnrealizedGainLossOnFairValueMeasurementOfConvertibleDebt" xlink:to="cntm_UnrealizedGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_UnrealizedGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of unrealized gain (loss) on change in fair value of convertible debt during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_UnrealizedGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrealized Gain (Loss) On Fair Value Measurement Of Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_UnrealizedGainLossOnFairValueMeasurementOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value of convertible debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryPartsAndComponentsNetOfReserves" xlink:label="us-gaap_InventoryPartsAndComponentsNetOfReserves" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryPartsAndComponentsNetOfReserves" xlink:to="us-gaap_InventoryPartsAndComponentsNetOfReserves_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryPartsAndComponentsNetOfReserves_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory, Parts and Components, Net of Reserves</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryPartsAndComponentsNetOfReserves_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Parts</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:label="us-gaap_InventoryFinishedGoodsNetOfReserves" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:to="us-gaap_InventoryFinishedGoodsNetOfReserves_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryFinishedGoodsNetOfReserves_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory, Finished Goods, Net of Reserves</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryFinishedGoodsNetOfReserves_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finished Goods</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:to="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Antidilutive Securities [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesNameDomain" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Antidilutive Securities, Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LegacyOptionsMember" xlink:label="cntm_LegacyOptionsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LegacyOptionsMember" xlink:to="cntm_LegacyOptionsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LegacyOptionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to legacy options.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LegacyOptionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Legacy Options [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LegacyOptionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Options</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LegacyWarrantsMember" xlink:label="cntm_LegacyWarrantsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LegacyWarrantsMember" xlink:to="cntm_LegacyWarrantsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LegacyWarrantsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to legacy warrants.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LegacyWarrantsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Legacy Warrants [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LegacyWarrantsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Warrants</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConvertibleDebtSecuritiesMember" xlink:label="us-gaap_ConvertibleDebtSecuritiesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConvertibleDebtSecuritiesMember" xlink:to="us-gaap_ConvertibleDebtSecuritiesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConvertibleDebtSecuritiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Debt Securities [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConvertibleDebtSecuritiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible notes payable that convert into common stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_IssuableSharesUponPotentialConversionOfConvertibleNotesMember" xlink:label="cntm_IssuableSharesUponPotentialConversionOfConvertibleNotesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IssuableSharesUponPotentialConversionOfConvertibleNotesMember" xlink:to="cntm_IssuableSharesUponPotentialConversionOfConvertibleNotesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IssuableSharesUponPotentialConversionOfConvertibleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represent the information of Issuable shares upon potential conversion of convertible notes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IssuableSharesUponPotentialConversionOfConvertibleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuable Shares Upon Potential Conversion Of Convertible Notes [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_IssuableSharesUponPotentialConversionOfConvertibleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuable shares upon potential conversion of convertible notes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:to="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Anti-dilutive effect</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockByClassTable" xlink:label="us-gaap_ScheduleOfStockByClassTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfStockByClassTable" xlink:to="us-gaap_ScheduleOfStockByClassTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock, Class of Stock [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockLineItems" xlink:label="us-gaap_ClassOfStockLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_ClassOfStockLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Cash" xlink:label="us-gaap_Cash" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Cash" xlink:to="us-gaap_Cash_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Cash_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Cash_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_Cash_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_WorkingCapitalDeficit" xlink:label="cntm_WorkingCapitalDeficit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_WorkingCapitalDeficit" xlink:to="cntm_WorkingCapitalDeficit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_WorkingCapitalDeficit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of working capital where the current assets is less than the current liabilities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_WorkingCapitalDeficit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Working Capital Deficit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_WorkingCapitalDeficit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Working capital deficit</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentDebtDefaultNumber" xlink:label="cntm_DebtInstrumentDebtDefaultNumber" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentDebtDefaultNumber" xlink:to="cntm_DebtInstrumentDebtDefaultNumber_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentDebtDefaultNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of debt instruments in which the entity is under default as of the reporting date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentDebtDefaultNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Debt Default, Number</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentDebtDefaultNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of debt instruments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:to="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Groups, Including Discontinued Operations [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:to="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain" xlink:to="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupsIncludingDiscontinuedOperationsNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_HvacBusinessAssetsAndOperationsMember" xlink:label="cntm_HvacBusinessAssetsAndOperationsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_HvacBusinessAssetsAndOperationsMember" xlink:to="cntm_HvacBusinessAssetsAndOperationsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_HvacBusinessAssetsAndOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to HVAC business assets and operations.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_HvacBusinessAssetsAndOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">HVAC Business Assets And Operations [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_HvacBusinessAssetsAndOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">HVAC business assets and operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationAxis" xlink:label="us-gaap_DisposalGroupClassificationAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupClassificationAxis" xlink:to="us-gaap_DisposalGroupClassificationAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupClassificationAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Classification [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationDomain" xlink:label="us-gaap_DisposalGroupClassificationDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupClassificationDomain" xlink:to="us-gaap_DisposalGroupClassificationDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupClassificationDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Classification [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupNotDiscontinuedOperationsMember" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupNotDiscontinuedOperationsMember" xlink:to="us-gaap_DisposalGroupNotDiscontinuedOperationsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Not Discontinued Operations [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal group, not discontinued operations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Continuing Operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets by Major Class [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Major Class Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NoncompeteAndNonSolicitAgreementsMember" xlink:label="cntm_NoncompeteAndNonSolicitAgreementsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NoncompeteAndNonSolicitAgreementsMember" xlink:to="cntm_NoncompeteAndNonSolicitAgreementsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NoncompeteAndNonSolicitAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Agreement in which one party agrees not to pursue a similar trade in competition with another party and non-solicit agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NoncompeteAndNonSolicitAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncompete and Non-solicit Agreements [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NoncompeteAndNonSolicitAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-compete and non-solicit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:to="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DISPOSALS</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash consideration received or receivable for the disposal of assets and liabilities, including discontinued operation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Cash Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupPercentageOfNonVotingNonDistributingEquityInterestRetained" xlink:label="cntm_DisposalGroupPercentageOfNonVotingNonDistributingEquityInterestRetained" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupPercentageOfNonVotingNonDistributingEquityInterestRetained" xlink:to="cntm_DisposalGroupPercentageOfNonVotingNonDistributingEquityInterestRetained_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupPercentageOfNonVotingNonDistributingEquityInterestRetained_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of non-voting, non-distributing equity interest retained by the company in a disposal group.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupPercentageOfNonVotingNonDistributingEquityInterestRetained_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Percentage Of Non-Voting, Non-Distributing Equity Interest Retained</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupPercentageOfNonVotingNonDistributingEquityInterestRetained_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of non-voting, non-distributing equity interest in ATS LLC</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupPercentageOfNetProceedsFromAssetsSold" xlink:label="cntm_DisposalGroupPercentageOfNetProceedsFromAssetsSold" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupPercentageOfNetProceedsFromAssetsSold" xlink:to="cntm_DisposalGroupPercentageOfNetProceedsFromAssetsSold_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupPercentageOfNetProceedsFromAssetsSold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of net proceeds receivable by the company if the asset is sold by the disposal group within the given time frame.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupPercentageOfNetProceedsFromAssetsSold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Percentage Of Net Proceeds From Assets Sold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupPercentageOfNetProceedsFromAssetsSold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of net proceeds receivable from ATS LLC</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupSaleOfTransferredAssetsPeriod" xlink:label="cntm_DisposalGroupSaleOfTransferredAssetsPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupSaleOfTransferredAssetsPeriod" xlink:to="cntm_DisposalGroupSaleOfTransferredAssetsPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupSaleOfTransferredAssetsPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period during which the transferred asset is required to be sold by the disposal group, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupSaleOfTransferredAssetsPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Sale Of Transferred Assets, Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupSaleOfTransferredAssetsPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period for selling assets</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupCovenantPeriod" xlink:label="cntm_DisposalGroupCovenantPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupCovenantPeriod" xlink:to="cntm_DisposalGroupCovenantPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupCovenantPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period during which the company has agreed with disposal group, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupCovenantPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Covenant Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupCovenantPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Covenant period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Goodwill</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying amount of goodwill</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationGoodwill1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposalStatementOfIncomeExtensibleList" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposalStatementOfIncomeExtensibleList" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposalStatementOfIncomeExtensibleList" xlink:to="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposalStatementOfIncomeExtensibleList_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposalStatementOfIncomeExtensibleList_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Not Discontinued Operation, Gain (Loss) on Disposal, Statement of Income or Comprehensive Income [Extensible Enumeration]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposalStatementOfIncomeExtensibleList_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Not Discontinued Operation, Gain (Loss) on Disposal, Statement of Income or Comprehensive Income [Extensible Enumeration]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GreenEnergyGainsMember" xlink:label="cntm_GreenEnergyGainsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GreenEnergyGainsMember" xlink:to="cntm_GreenEnergyGainsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GreenEnergyGainsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Green Energy Gains ("GEG").</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GreenEnergyGainsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Green Energy Gains [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GreenEnergyGainsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Green Energy Gains</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember" xlink:label="us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember" xlink:to="us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Disposed of by Sale, Not Discontinued Operations [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposed by sale</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration" xlink:to="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangibles assets, consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total consideration</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationCashConsiderationReceived" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsiderationReceived" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsiderationReceived" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsiderationReceived_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsiderationReceived_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash consideration received or receivable for the disposal of assets and liabilities, including discontinued operation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsiderationReceived_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Cash Consideration Received</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashConsiderationReceived_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash consideration</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsideration" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsideration" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of holdback consideration received or receivable for the disposal of assets and liabilities, including discontinued operation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Including Discontinued Operation, Holdback Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration placed into holdback</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasableUponCompletionOfDeliverySchedule" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasableUponCompletionOfDeliverySchedule" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasableUponCompletionOfDeliverySchedule" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasableUponCompletionOfDeliverySchedule_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasableUponCompletionOfDeliverySchedule_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of disclosure holdback consideration releasable upon the Company's delivery of a completed disclosure schedule.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasableUponCompletionOfDeliverySchedule_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Including Discontinued Operation, Holdback Consideration Releasable upon Completion of Delivery Schedule</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasableUponCompletionOfDeliverySchedule_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Holdback releasable upon delivery</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasable90DaysAfterClosing" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasable90DaysAfterClosing" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasable90DaysAfterClosing" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasable90DaysAfterClosing_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasable90DaysAfterClosing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of general holdback consideration releasable 90 days after closing</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasable90DaysAfterClosing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Including Discontinued Operation, Holdback Consideration Releasable 90 Days after Closing</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationHoldbackConsiderationReleasable90DaysAfterClosing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Holdback releasable after 90 days</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationCashAndHoldbackConsideration" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashAndHoldbackConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationCashAndHoldbackConsideration" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationCashAndHoldbackConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashAndHoldbackConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash and holdback consideration received or receivable for the disposal of assets and liabilities, including discontinued operation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashAndHoldbackConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group Including Discontinued Operation, Cash and Holdback Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationCashAndHoldbackConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Full consideration at closing</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationNetIdentifiableAssets" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNetIdentifiableAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationNetIdentifiableAssets" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationNetIdentifiableAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNetIdentifiableAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount classified as net identifiable assets attributable to disposal group held for sale or disposed of.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNetIdentifiableAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Net Identifiable Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNetIdentifiableAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net identifiable assets disposed</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupTransitionalAssistancePeriod" xlink:label="cntm_DisposalGroupTransitionalAssistancePeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupTransitionalAssistancePeriod" xlink:to="cntm_DisposalGroupTransitionalAssistancePeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupTransitionalAssistancePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the period of transitional assistance with the disposal group.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupTransitionalAssistancePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Transitional Assistance Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupTransitionalAssistancePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transitional assistance period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupNonCompeteCovenantPeriod" xlink:label="cntm_DisposalGroupNonCompeteCovenantPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupNonCompeteCovenantPeriod" xlink:to="cntm_DisposalGroupNonCompeteCovenantPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupNonCompeteCovenantPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period during which the company has agreed not to compete with disposal group, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupNonCompeteCovenantPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Non-Compete Covenant Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupNonCompeteCovenantPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-competed covenant period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:to="us-gaap_ScheduleOfEquityMethodInvestmentsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment, Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain" xlink:label="srt_EquityMethodInvesteeNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_EquityMethodInvesteeNameDomain" xlink:to="srt_EquityMethodInvesteeNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_EquityMethodInvesteeNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment, Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SunSolarLlcMember" xlink:label="cntm_SunSolarLlcMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SunSolarLlcMember" xlink:to="cntm_SunSolarLlcMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SunSolarLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Sun Solar LLC.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SunSolarLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sun Solar LLC [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SunSolarLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sun Solar LLC</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LegalEntityAxis" xlink:label="dei_LegalEntityAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_LegalEntityAxis" xlink:to="dei_LegalEntityAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_LegalEntityAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Legal Entity [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityDomain" xlink:label="dei_EntityDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityDomain" xlink:to="dei_EntityDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">All Entities [Member]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipAxis" xlink:label="srt_OwnershipAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_OwnershipAxis" xlink:to="srt_OwnershipAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_OwnershipAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain" xlink:label="srt_OwnershipDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_OwnershipDomain" xlink:to="srt_OwnershipDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_OwnershipDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SellerMember" xlink:label="cntm_SellerMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SellerMember" xlink:to="cntm_SellerMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SellerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents of sole member (the "Seller").</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SellerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Seller [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SellerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Seller</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:to="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Equity Method Investments [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">RELATED PARTY TRANSACTIONS</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">INVESTMENT IN SUN SOLAR - EQUITY METHOD</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EquityMethodInvestmentNumberOfMembershipInterestsAcquired" xlink:label="cntm_EquityMethodInvestmentNumberOfMembershipInterestsAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquityMethodInvestmentNumberOfMembershipInterestsAcquired" xlink:to="cntm_EquityMethodInvestmentNumberOfMembershipInterestsAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquityMethodInvestmentNumberOfMembershipInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of membership interests acquired in investments accounted for under the equity method of accounting.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquityMethodInvestmentNumberOfMembershipInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Number Of Membership Interests Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EquityMethodInvestmentNumberOfMembershipInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of membership interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:to="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Ownership Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership Percentage</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LimitedPartnersCapitalAccountUnitsIssued" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LimitedPartnersCapitalAccountUnitsIssued" xlink:to="us-gaap_LimitedPartnersCapitalAccountUnitsIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Limited Partners' Capital Account, Units Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Units issued</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProductSalesRevenue" xlink:label="cntm_ProductSalesRevenue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProductSalesRevenue" xlink:to="cntm_ProductSalesRevenue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProductSalesRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The Amount of product sales revenue for the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProductSalesRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Product Sales Revenue</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProductSalesRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of product sales revenue</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xlink:label="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest" xlink:to="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Limited Liability Company or Limited Partnership, Members or Limited Partners, Ownership Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPMembersOrLimitedPartnersOwnershipInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Partners ownership percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodSharesEquityMethodInvestment" xlink:label="cntm_StockIssuedDuringPeriodSharesEquityMethodInvestment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesEquityMethodInvestment" xlink:to="cntm_StockIssuedDuringPeriodSharesEquityMethodInvestment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of stock issued during the period pursuant to an equity method investment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Equity Method Investment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesEquityMethodInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of stock issued during the period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EquityMethodInvestmentInitialRecognitionCarryingAmount" xlink:label="cntm_EquityMethodInvestmentInitialRecognitionCarryingAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquityMethodInvestmentInitialRecognitionCarryingAmount" xlink:to="cntm_EquityMethodInvestmentInitialRecognitionCarryingAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquityMethodInvestmentInitialRecognitionCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Initial carrying amount of equity method investment recognized in the books.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquityMethodInvestmentInitialRecognitionCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Initial Recognition, Carrying Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EquityMethodInvestmentInitialRecognitionCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Initial carrying amount of the investment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:to="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Asset, Finite-Lived [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CustomerRelationshipsMember" xlink:label="us-gaap_CustomerRelationshipsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CustomerRelationshipsMember" xlink:to="us-gaap_CustomerRelationshipsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CustomerRelationshipsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer Relationships [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CustomerRelationshipsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer relationships</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CustomerRelationshipsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customers relationship</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TradeNamesMember" xlink:label="us-gaap_TradeNamesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TradeNamesMember" xlink:to="us-gaap_TradeNamesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TradeNamesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Trade Names [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TradeNamesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Trade name</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_TradeNamesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Trade Names</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncompeteAgreementsMember" xlink:label="us-gaap_NoncompeteAgreementsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncompeteAgreementsMember" xlink:to="us-gaap_NoncompeteAgreementsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NoncompeteAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncompete Agreements [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NoncompeteAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncompetition agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NoncompeteAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncompetition Agreements</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntellectualPropertyMember" xlink:label="us-gaap_IntellectualPropertyMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IntellectualPropertyMember" xlink:to="us-gaap_IntellectualPropertyMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IntellectualPropertyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intellectual Property [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IntellectualPropertyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intellectual property</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_IntellectualPropertyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intellectual Property</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProprietaryTechnologyMember" xlink:label="cntm_ProprietaryTechnologyMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProprietaryTechnologyMember" xlink:to="cntm_ProprietaryTechnologyMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProprietaryTechnologyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to proprietary technology.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProprietaryTechnologyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proprietary Technology [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProprietaryTechnologyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible assets: Proprietary Technology</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComputerSoftwareIntangibleAssetMember" xlink:label="us-gaap_ComputerSoftwareIntangibleAssetMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComputerSoftwareIntangibleAssetMember" xlink:to="us-gaap_ComputerSoftwareIntangibleAssetMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComputerSoftwareIntangibleAssetMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Computer Software, Intangible Asset [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ComputerSoftwareIntangibleAssetMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Internally developed software</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ComputerSoftwareIntangibleAssetMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Internally Developed Software</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PatentsMember" xlink:label="us-gaap_PatentsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PatentsMember" xlink:to="us-gaap_PatentsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PatentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Patents [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PatentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Assets: Patent</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DevelopedTechnologyRightsMember" xlink:label="us-gaap_DevelopedTechnologyRightsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DevelopedTechnologyRightsMember" xlink:to="us-gaap_DevelopedTechnologyRightsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DevelopedTechnologyRightsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Developed Technology Rights [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DevelopedTechnologyRightsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Developed technologies</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DevelopedTechnologyRightsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Developed technology</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TechnologyBasedIntangibleAssetsMember" xlink:label="us-gaap_TechnologyBasedIntangibleAssetsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TechnologyBasedIntangibleAssetsMember" xlink:to="us-gaap_TechnologyBasedIntangibleAssetsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TechnologyBasedIntangibleAssetsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Technology-Based Intangible Assets [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TechnologyBasedIntangibleAssetsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquired technology</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_TechnologyBasedIntangibleAssetsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquired technologies</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:label="us-gaap_FiniteLivedIntangibleAssetsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:to="us-gaap_FiniteLivedIntangibleAssetsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">INTANGIBLE ASSETS, NET</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">GOODWILL AND INTANGIBLE ASSETS, NET</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:label="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:to="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Remaining Amortization Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Remaining Amortization Period (years)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsGross" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsGross" xlink:to="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross Amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Accumulated Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated Amortization</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsNet" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DevelopedTechnologyMember" xlink:label="cntm_DevelopedTechnologyMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DevelopedTechnologyMember" xlink:to="cntm_DevelopedTechnologyMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DevelopedTechnologyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to developed technology.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DevelopedTechnologyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Developed Technology [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DevelopedTechnologyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Developed Technology</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReportingUnitAxis" xlink:label="us-gaap_ReportingUnitAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ReportingUnitAxis" xlink:to="us-gaap_ReportingUnitAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ReportingUnitAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reporting Unit [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReportingUnitDomain" xlink:label="us-gaap_ReportingUnitDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ReportingUnitDomain" xlink:to="us-gaap_ReportingUnitDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ReportingUnitDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reporting Unit [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_OwnedServiceNetworkSegmentMember" xlink:label="cntm_OwnedServiceNetworkSegmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_OwnedServiceNetworkSegmentMember" xlink:to="cntm_OwnedServiceNetworkSegmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_OwnedServiceNetworkSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the entity's Owned Service Network segment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OwnedServiceNetworkSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Owned Service Network Segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_OwnedServiceNetworkSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Owned Service Network</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueOfReportingUnitAnnualImpairmentTestDiscountRate" xlink:label="cntm_FairValueOfReportingUnitAnnualImpairmentTestDiscountRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueOfReportingUnitAnnualImpairmentTestDiscountRate" xlink:to="cntm_FairValueOfReportingUnitAnnualImpairmentTestDiscountRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueOfReportingUnitAnnualImpairmentTestDiscountRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Discount rate used to determine the present value of estimated future cash flows.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueOfReportingUnitAnnualImpairmentTestDiscountRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Of Reporting Unit, Annual Impairment Test, Discount Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueOfReportingUnitAnnualImpairmentTestDiscountRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Annual impairment test, discount rate (in percentage)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueOfReportingUnitSensitivityAnalysisPercentIncreaseDecreaseInDiscountRate" xlink:label="cntm_FairValueOfReportingUnitSensitivityAnalysisPercentIncreaseDecreaseInDiscountRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueOfReportingUnitSensitivityAnalysisPercentIncreaseDecreaseInDiscountRate" xlink:to="cntm_FairValueOfReportingUnitSensitivityAnalysisPercentIncreaseDecreaseInDiscountRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueOfReportingUnitSensitivityAnalysisPercentIncreaseDecreaseInDiscountRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of increase (decrease) in discount rate under sensitivity analysis.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueOfReportingUnitSensitivityAnalysisPercentIncreaseDecreaseInDiscountRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Of Reporting Unit, Sensitivity Analysis, Percent, Increase (Decrease) in Discount Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueOfReportingUnitSensitivityAnalysisPercentIncreaseDecreaseInDiscountRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of increase (decrease) in discount rate</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueOfReportingUnitSensitivityAnalysisChangeInFairValueImpactOfFivePercentIncreaseDecreaseInDiscountRate" xlink:label="cntm_FairValueOfReportingUnitSensitivityAnalysisChangeInFairValueImpactOfFivePercentIncreaseDecreaseInDiscountRate" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueOfReportingUnitSensitivityAnalysisChangeInFairValueImpactOfFivePercentIncreaseDecreaseInDiscountRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The hypothetical financial impact of a five percent increase (decrease) in discount rate on the fair value of reporting unit as of the balance sheet date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueOfReportingUnitSensitivityAnalysisChangeInFairValueImpactOfFivePercentIncreaseDecreaseInDiscountRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Of Reporting Unit, Sensitivity Analysis, Change in Fair Value, Impact of Five Percent Increase Decrease in Discount Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueOfReportingUnitSensitivityAnalysisChangeInFairValueImpactOfFivePercentIncreaseDecreaseInDiscountRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value, impact of 5% increase (decrease) in discount rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReportingUnitPercentageOfFairValueInExcessOfCarryingAmount" xlink:label="us-gaap_ReportingUnitPercentageOfFairValueInExcessOfCarryingAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ReportingUnitPercentageOfFairValueInExcessOfCarryingAmount" xlink:to="us-gaap_ReportingUnitPercentageOfFairValueInExcessOfCarryingAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ReportingUnitPercentageOfFairValueInExcessOfCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reporting Unit, Percentage of Fair Value in Excess of Carrying Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ReportingUnitPercentageOfFairValueInExcessOfCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of estimated fair value exceeded its carrying amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill" xlink:to="us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment of Intangible Assets (Excluding Goodwill)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment loss</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ImpairmentIntangibleAssetStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xlink:label="us-gaap_ImpairmentIntangibleAssetStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ImpairmentIntangibleAssetStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xlink:to="us-gaap_ImpairmentIntangibleAssetStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ImpairmentIntangibleAssetStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment, Intangible Asset, Statement of Income or Comprehensive Income [Extensible Enumeration]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ImpairmentOfGoodwillAffectingIdentifiableIntangibleAssets" xlink:label="cntm_ImpairmentOfGoodwillAffectingIdentifiableIntangibleAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ImpairmentOfGoodwillAffectingIdentifiableIntangibleAssets" xlink:to="cntm_ImpairmentOfGoodwillAffectingIdentifiableIntangibleAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ImpairmentOfGoodwillAffectingIdentifiableIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of impairment of goodwill affecting identifiable intangible assets.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ImpairmentOfGoodwillAffectingIdentifiableIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment Of Goodwill Affecting Identifiable Intangible Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ImpairmentOfGoodwillAffectingIdentifiableIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment charge on goodwill</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:to="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Useful Life</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated useful life</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfIntangibleAssets" xlink:label="us-gaap_AmortizationOfIntangibleAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AmortizationOfIntangibleAssets" xlink:to="us-gaap_AmortizationOfIntangibleAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of Intangible Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of intangible assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalizedComputerSoftwareGross" xlink:label="us-gaap_CapitalizedComputerSoftwareGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CapitalizedComputerSoftwareGross" xlink:to="us-gaap_CapitalizedComputerSoftwareGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CapitalizedComputerSoftwareGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capitalized Computer Software, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CapitalizedComputerSoftwareGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capitalized costs, internally developed software</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalizedComputerSoftwareNet" xlink:label="us-gaap_CapitalizedComputerSoftwareNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CapitalizedComputerSoftwareNet" xlink:to="us-gaap_CapitalizedComputerSoftwareNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CapitalizedComputerSoftwareNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capitalized Computer Software, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CapitalizedComputerSoftwareNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capitalized computer software costs</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AmortizationOfCapitalizedComputerSoftware" xlink:label="cntm_AmortizationOfCapitalizedComputerSoftware" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AmortizationOfCapitalizedComputerSoftware" xlink:to="cntm_AmortizationOfCapitalizedComputerSoftware_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AmortizationOfCapitalizedComputerSoftware_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for capitalized computer software costs.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AmortizationOfCapitalizedComputerSoftware_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization Of Capitalized Computer Software</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AmortizationOfCapitalizedComputerSoftware_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of capitalized computer software</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationRemainderOfFiscalYear" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationRemainderOfFiscalYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationRemainderOfFiscalYear" xlink:to="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationRemainderOfFiscalYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationRemainderOfFiscalYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in remainder of current fiscal year.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationRemainderOfFiscalYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, Remainder of Fiscal Year</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationRemainderOfFiscalYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026 (nine months)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne" xlink:to="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo" xlink:to="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree" xlink:to="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2029</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour" xlink:to="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2030</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2029</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFive" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFive" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFive" xlink:to="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFive_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in fifth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2030</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFour" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFour" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFour" xlink:to="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFour_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in after fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, after Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Thereafter</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFive" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFive" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFive" xlink:to="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFive_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for assets, excluding internally developed software, financial assets and goodwill, lacking physical substance with finite life expected to be recognized in after fifth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset Excluding Internally Developed Software, Expected Amortization, after Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FiniteLivedIntangibleAssetExcludingInternallyDevelopedSoftwareExpectedAmortizationAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Thereafter</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2026Member" xlink:label="cntm_ConvertibleNotes2026Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026Member" xlink:to="cntm_ConvertibleNotes2026Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to 2026 Convertible Notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes, 2026 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026 Convertible Notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2025Member" xlink:label="cntm_ConvertibleNotes2025Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2025Member" xlink:to="cntm_ConvertibleNotes2025Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to 2025 Convertible Notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes, 2025 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2025 Convertible Notes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_ConvertibleNotes2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2025 convertible notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_Assumed2024NotesMember" xlink:label="cntm_Assumed2024NotesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_Assumed2024NotesMember" xlink:to="cntm_Assumed2024NotesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_Assumed2024NotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to assumed 2024 notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_Assumed2024NotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assumed 2024 Notes [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_Assumed2024NotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assumed 2024 Note</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_Assumed2024NotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assumed 2024 notes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability" xlink:label="us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability" xlink:to="us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Embedded Derivative, Fair Value of Embedded Derivative Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EmbeddedDerivativeFairValueOfEmbeddedDerivativeLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative liability</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2024Member" xlink:label="cntm_ConvertibleNotes2024Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2024Member" xlink:to="cntm_ConvertibleNotes2024Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to 2024 Convertible Notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2024 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2024 Convertible Notes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_ConvertibleNotes2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2024 convertible notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SettlementAndTerminationAgreementMember" xlink:label="cntm_SettlementAndTerminationAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementAndTerminationAgreementMember" xlink:to="cntm_SettlementAndTerminationAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAndTerminationAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to settlement and termination agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementAndTerminationAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement And Termination Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAndTerminationAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement and Termination Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_SettlementAndTerminationAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Yorkville Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StandbyEquityPurchaseAgreementMember" xlink:label="cntm_StandbyEquityPurchaseAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StandbyEquityPurchaseAgreementMember" xlink:to="cntm_StandbyEquityPurchaseAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StandbyEquityPurchaseAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to standby equity purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StandbyEquityPurchaseAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Standby Equity Purchase Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StandbyEquityPurchaseAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Standby equity purchase agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementBasisAxis" xlink:label="us-gaap_FairValueByMeasurementBasisAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByMeasurementBasisAxis" xlink:to="us-gaap_FairValueByMeasurementBasisAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByMeasurementBasisAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Basis [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:label="us-gaap_PortionAtFairValueFairValueDisclosureMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="us-gaap_PortionAtFairValueFairValueDisclosureMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PortionAtFairValueFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Portion at Fair Value Measurement [Member]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:label="us-gaap_CarryingReportedAmountFairValueDisclosureMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="us-gaap_CarryingReportedAmountFairValueDisclosureMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CarryingReportedAmountFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reported Value Measurement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CarryingReportedAmountFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying Amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:label="us-gaap_EstimateOfFairValueFairValueDisclosureMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="us-gaap_EstimateOfFairValueFairValueDisclosureMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EstimateOfFairValueFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimate of Fair Value Measurement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EstimateOfFairValueFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated Fair Value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CounterpartyNameAxis" xlink:label="srt_CounterpartyNameAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_CounterpartyNameAxis" xlink:to="srt_CounterpartyNameAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_CounterpartyNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Counterparty Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RepurchaseAgreementCounterpartyNameDomain" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Counterparty Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_YaIiPnLimitedMember" xlink:label="cntm_YaIiPnLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_YaIiPnLimitedMember" xlink:to="cntm_YaIiPnLimitedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_YaIiPnLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to YA II PN, Limited ("Yorkville").</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_YaIiPnLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">YA II PN, Limited [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_YaIiPnLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Yorkville</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_VanquishAndLabrysMember" xlink:label="cntm_VanquishAndLabrysMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_VanquishAndLabrysMember" xlink:to="cntm_VanquishAndLabrysMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_VanquishAndLabrysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Vanquish and Labrys.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_VanquishAndLabrysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vanquish and Labrys [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_VanquishAndLabrysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vanquish and Labrys</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_OtherPartiesMember" xlink:label="cntm_OtherPartiesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_OtherPartiesMember" xlink:to="cntm_OtherPartiesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_OtherPartiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to other parties.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OtherPartiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Parties [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_OtherPartiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other parties</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_VanquishMember" xlink:label="cntm_VanquishMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_VanquishMember" xlink:to="cntm_VanquishMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_VanquishMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Vanquish.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_VanquishMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vanquish [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_VanquishMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vanquish</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementScenarioAxis" xlink:label="srt_StatementScenarioAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_StatementScenarioAxis" xlink:to="srt_StatementScenarioAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_StatementScenarioAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Scenario [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScenarioUnspecifiedDomain" xlink:label="srt_ScenarioUnspecifiedDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ScenarioUnspecifiedDomain" xlink:to="srt_ScenarioUnspecifiedDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ScenarioUnspecifiedDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Scenario [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtConversionOptionUnavailableMember" xlink:label="cntm_DebtConversionOptionUnavailableMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtConversionOptionUnavailableMember" xlink:to="cntm_DebtConversionOptionUnavailableMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtConversionOptionUnavailableMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the scenario where the debt conversion option is not available.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtConversionOptionUnavailableMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Conversion Option Unavailable [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtConversionOptionUnavailableMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Conversion Option Unavailable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_InEventOfConsummationOfIpoMember" xlink:label="cntm_InEventOfConsummationOfIpoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_InEventOfConsummationOfIpoMember" xlink:to="cntm_InEventOfConsummationOfIpoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_InEventOfConsummationOfIpoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">In The Event Of Consummation of IPO [Member]Represents the information pertaining to event of consummation of IPO.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_InEventOfConsummationOfIpoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">In The Event Of Consummation of IPO [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_InEventOfConsummationOfIpoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">In the event of consummation of IPO</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeAxis" xlink:label="us-gaap_SubsequentEventTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTypeAxis" xlink:to="us-gaap_SubsequentEventTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event Type [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeDomain" xlink:label="us-gaap_SubsequentEventTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTypeDomain" xlink:to="us-gaap_SubsequentEventTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event Type [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventMember" xlink:label="us-gaap_SubsequentEventMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventMember" xlink:to="us-gaap_SubsequentEventMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent events</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentConvertibleNumber" xlink:label="cntm_DebtInstrumentConvertibleNumber" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConvertibleNumber" xlink:to="cntm_DebtInstrumentConvertibleNumber_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConvertibleNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of convertible debt notes issued by the entity during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConvertibleNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Number</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConvertibleNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of individuals issued</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentFaceAmount" xlink:label="us-gaap_DebtInstrumentFaceAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentFaceAmount" xlink:to="us-gaap_DebtInstrumentFaceAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Face Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Principal amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of pre-paid advance</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromNotesPayable" xlink:label="us-gaap_ProceedsFromNotesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromNotesPayable" xlink:to="us-gaap_ProceedsFromNotesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Notes Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from the issuance of convertible notes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProceedsFromNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross proceeds</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Interest Rate, Stated Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest rate (in percentage)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest rate (in percent)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTerm" xlink:label="us-gaap_DebtInstrumentTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentTerm" xlink:to="us-gaap_DebtInstrumentTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maturity Date (from issuance date)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentConvertibleOptionalConversionTerm" xlink:label="cntm_DebtInstrumentConvertibleOptionalConversionTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConvertibleOptionalConversionTerm" xlink:to="cntm_DebtInstrumentConvertibleOptionalConversionTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConvertibleOptionalConversionTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the optional conversion period for notes payable.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConvertibleOptionalConversionTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Optional Conversion Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConvertibleOptionalConversionTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Optional conversion period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:label="us-gaap_DebtInstrumentConvertibleConversionPrice1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:to="us-gaap_DebtInstrumentConvertibleConversionPrice1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentConvertibleConversionPrice1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Conversion Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentConvertibleConversionPrice1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument convertible conversion price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentConvertibleConversionPrice1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion Price (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConvertibleDebtFairValueDisclosures" xlink:label="us-gaap_ConvertibleDebtFairValueDisclosures" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConvertibleDebtFairValueDisclosures" xlink:to="us-gaap_ConvertibleDebtFairValueDisclosures_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConvertibleDebtFairValueDisclosures_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Debt, Fair Value Disclosures</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_ConvertibleDebtFairValueDisclosures_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total fair value of Pre-Paid Advance Obligation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConvertibleDebtFairValueDisclosures_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ConvertibleDebtFairValueDisclosures_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of convertible debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentInterestRateOnEventOfDefaultPercentage" xlink:label="cntm_DebtInstrumentInterestRateOnEventOfDefaultPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentInterestRateOnEventOfDefaultPercentage" xlink:to="cntm_DebtInstrumentInterestRateOnEventOfDefaultPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentInterestRateOnEventOfDefaultPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of interest rate charged on the funds borrowed upon occurrence of default under the debt agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentInterestRateOnEventOfDefaultPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Interest Rate, On Event of Default, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentInterestRateOnEventOfDefaultPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest rate at event of default</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentConvertibleSharesIssuable" xlink:label="cntm_DebtInstrumentConvertibleSharesIssuable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConvertibleSharesIssuable" xlink:to="cntm_DebtInstrumentConvertibleSharesIssuable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConvertibleSharesIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issuable to the holder of the debt instrument if the debt was converted into equity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConvertibleSharesIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Shares Issuable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConvertibleSharesIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock convertible notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProceedsFromNotesPayableNet" xlink:label="cntm_ProceedsFromNotesPayableNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromNotesPayableNet" xlink:to="cntm_ProceedsFromNotesPayableNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromNotesPayableNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The net cash inflow after reduction of issuance and financing costs, from a borrowing supported by a written promise to pay an obligation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromNotesPayableNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Notes Payable, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsFromNotesPayableNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from notes payable net</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentOriginalIssueDiscountPercentage" xlink:label="cntm_DebtInstrumentOriginalIssueDiscountPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentOriginalIssueDiscountPercentage" xlink:to="cntm_DebtInstrumentOriginalIssueDiscountPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentOriginalIssueDiscountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage rate of the original issue discount on the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentOriginalIssueDiscountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Original Issue Discount, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentOriginalIssueDiscountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage rate of the original issue discount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentNoConversionPeriod" xlink:label="cntm_DebtInstrumentNoConversionPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentNoConversionPeriod" xlink:to="cntm_DebtInstrumentNoConversionPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentNoConversionPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The period of time following the receipt of a contractually required payment during which the holder of a debt instrument is prohibited from exercising conversion or equity issuance rights under the applicable agreement, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentNoConversionPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, No Conversion Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentNoConversionPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">No conversion period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentTerminationFeesSharesIssuedValue" xlink:label="cntm_DebtInstrumentTerminationFeesSharesIssuedValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentTerminationFeesSharesIssuedValue" xlink:to="cntm_DebtInstrumentTerminationFeesSharesIssuedValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentTerminationFeesSharesIssuedValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of shares issued as debt instrument termination fees.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentTerminationFeesSharesIssuedValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument Termination Fees, Shares Issued, Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentTerminationFeesSharesIssuedValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate value of share issued (Termination fee)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger" xlink:label="us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger" xlink:to="us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Threshold Percentage of Stock Price Trigger</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SEPA Convertible Note, purchase price (being the % of the lowest daily VWAP of common stock on Nasdaq during the 10 consecutive Trading Days)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentConvertibleThresholdPercentageOfStockPriceTrigger_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold percentage of stock price trigger</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentConvertibleThresholdConsecutiveTradingDays1" xlink:label="us-gaap_DebtInstrumentConvertibleThresholdConsecutiveTradingDays1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentConvertibleThresholdConsecutiveTradingDays1" xlink:to="us-gaap_DebtInstrumentConvertibleThresholdConsecutiveTradingDays1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentConvertibleThresholdConsecutiveTradingDays1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Threshold Consecutive Trading Days</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentConvertibleThresholdConsecutiveTradingDays1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of consecutive trading days prior to conversion date (in days)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_RepaymentOfPrincipalAmountOfDebt" xlink:label="cntm_RepaymentOfPrincipalAmountOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RepaymentOfPrincipalAmountOfDebt" xlink:to="cntm_RepaymentOfPrincipalAmountOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RepaymentOfPrincipalAmountOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash outflow associated with repayment of principal amount of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RepaymentOfPrincipalAmountOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayment Of Principal Amount Of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RepaymentOfPrincipalAmountOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayment of principal amount of debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_RepaymentsOfInterestPaidNet" xlink:label="cntm_RepaymentsOfInterestPaidNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RepaymentsOfInterestPaidNet" xlink:to="cntm_RepaymentsOfInterestPaidNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RepaymentsOfInterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash paid for interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RepaymentsOfInterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments Of Interest Paid Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RepaymentsOfInterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid for interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:label="us-gaap_PaymentsOfDebtExtinguishmentCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:to="us-gaap_PaymentsOfDebtExtinguishmentCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfDebtExtinguishmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment for Debt Extinguishment or Debt Prepayment Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsOfDebtExtinguishmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash payment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtConversionOriginalDebtPrincipalAmount" xlink:label="cntm_DebtConversionOriginalDebtPrincipalAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtConversionOriginalDebtPrincipalAmount" xlink:to="cntm_DebtConversionOriginalDebtPrincipalAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtConversionOriginalDebtPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Principal amount of original debt converted during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtConversionOriginalDebtPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Conversion, Original Debt, Principal, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtConversionOriginalDebtPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Original debt, principal</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtConversionOriginalDebtAccruedInterestAmount" xlink:label="cntm_DebtConversionOriginalDebtAccruedInterestAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtConversionOriginalDebtAccruedInterestAmount" xlink:to="cntm_DebtConversionOriginalDebtAccruedInterestAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtConversionOriginalDebtAccruedInterestAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued interest amount of original debt converted during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtConversionOriginalDebtAccruedInterestAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Conversion, Original Debt, Accrued Interest, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtConversionOriginalDebtAccruedInterestAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Original debt, accrued interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:label="us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:to="us-gaap_DebtConversionConvertedInstrumentSharesIssued1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtConversionConvertedInstrumentSharesIssued1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Conversion, Converted Instrument, Shares Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtConversionConvertedInstrumentSharesIssued1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion of debt to shares</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentConvertibleStockPriceTrigger" xlink:label="us-gaap_DebtInstrumentConvertibleStockPriceTrigger" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentConvertibleStockPriceTrigger" xlink:to="us-gaap_DebtInstrumentConvertibleStockPriceTrigger_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentConvertibleStockPriceTrigger_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Stock Price Trigger</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentConvertibleStockPriceTrigger_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SEPA Convertible Note, variable price (in $ per share)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentConvertibleStockPriceTrigger_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SEPA Convertible Note, floor price (in $ per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesPayable" xlink:label="us-gaap_NotesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesPayable" xlink:to="us-gaap_NotesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssued1" xlink:label="us-gaap_StockIssued1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssued1" xlink:to="us-gaap_StockIssued1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssued1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockIssued1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of the shares issued</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PercentageOfGrossProceedsFromSaleOfEquityOrEquityDerivativeInstrumentToBePaidTowardsNote" xlink:label="cntm_PercentageOfGrossProceedsFromSaleOfEquityOrEquityDerivativeInstrumentToBePaidTowardsNote" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PercentageOfGrossProceedsFromSaleOfEquityOrEquityDerivativeInstrumentToBePaidTowardsNote" xlink:to="cntm_PercentageOfGrossProceedsFromSaleOfEquityOrEquityDerivativeInstrumentToBePaidTowardsNote_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PercentageOfGrossProceedsFromSaleOfEquityOrEquityDerivativeInstrumentToBePaidTowardsNote_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of gross proceeds from sale of equity or equity derivative instruments to be paid by the entity towards the note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PercentageOfGrossProceedsFromSaleOfEquityOrEquityDerivativeInstrumentToBePaidTowardsNote_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage Of Gross Proceeds From Sale Of Equity Or Equity Derivative Instrument to be Paid Towards Note</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PercentageOfGrossProceedsFromSaleOfEquityOrEquityDerivativeInstrumentToBePaidTowardsNote_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of gross proceeds</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtConversionNumberOfDaysForConversionOptionPriorToMaturity" xlink:label="cntm_DebtConversionNumberOfDaysForConversionOptionPriorToMaturity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtConversionNumberOfDaysForConversionOptionPriorToMaturity" xlink:to="cntm_DebtConversionNumberOfDaysForConversionOptionPriorToMaturity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtConversionNumberOfDaysForConversionOptionPriorToMaturity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of days prior to maturity in which the conversion option of the debt instrument can be exercised by the holder.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtConversionNumberOfDaysForConversionOptionPriorToMaturity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Conversion, Number Of Days For Conversion Option Prior To Maturity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtConversionNumberOfDaysForConversionOptionPriorToMaturity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maturity date</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ThresholdDaysOfTrailingVolumeWeightedAveragePriceConsideredForConversion" xlink:label="cntm_ThresholdDaysOfTrailingVolumeWeightedAveragePriceConsideredForConversion" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ThresholdDaysOfTrailingVolumeWeightedAveragePriceConsideredForConversion" xlink:to="cntm_ThresholdDaysOfTrailingVolumeWeightedAveragePriceConsideredForConversion_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ThresholdDaysOfTrailingVolumeWeightedAveragePriceConsideredForConversion_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold days of trailing volume weighted average price considered for conversion of the note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ThresholdDaysOfTrailingVolumeWeightedAveragePriceConsideredForConversion_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold Days Of Trailing Volume Weighted Average Price Considered For Conversion</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ThresholdDaysOfTrailingVolumeWeightedAveragePriceConsideredForConversion_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold days of trailing volume</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PaymentsOfInitialMandatoryPaymentOfDebt" xlink:label="cntm_PaymentsOfInitialMandatoryPaymentOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentsOfInitialMandatoryPaymentOfDebt" xlink:to="cntm_PaymentsOfInitialMandatoryPaymentOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentsOfInitialMandatoryPaymentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The cash outflow for the initial mandatory payments of the debt instrument made by the entity during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentsOfInitialMandatoryPaymentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments Of Initial Mandatory Payment Of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PaymentsOfInitialMandatoryPaymentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Initial mandatory payments of the debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentInitialMandatoryPaymentRequired" xlink:label="cntm_DebtInstrumentInitialMandatoryPaymentRequired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentInitialMandatoryPaymentRequired" xlink:to="cntm_DebtInstrumentInitialMandatoryPaymentRequired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentInitialMandatoryPaymentRequired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The initial mandatory payment to be made by the entity as per the terms of the debt instrument during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentInitialMandatoryPaymentRequired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Initial Mandatory Payment Required</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentInitialMandatoryPaymentRequired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Initial mandatory payment required</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentInitialMandatoryPaymentPeriodFromEffectiveDate" xlink:label="cntm_DebtInstrumentInitialMandatoryPaymentPeriodFromEffectiveDate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentInitialMandatoryPaymentPeriodFromEffectiveDate" xlink:to="cntm_DebtInstrumentInitialMandatoryPaymentPeriodFromEffectiveDate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentInitialMandatoryPaymentPeriodFromEffectiveDate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The period from the effective date within which the initial mandatory payment for the debt instrument is required to be made, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentInitialMandatoryPaymentPeriodFromEffectiveDate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Initial Mandatory Payment, Period From Effective Date</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentInitialMandatoryPaymentPeriodFromEffectiveDate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Initial mandatory payment period from effective date</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentPrepaymentDiscountPercentage" xlink:label="cntm_DebtInstrumentPrepaymentDiscountPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentPrepaymentDiscountPercentage" xlink:to="cntm_DebtInstrumentPrepaymentDiscountPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentPrepaymentDiscountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of discount received by the entity on prepayment of debt as per the terms of the agreement for the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentPrepaymentDiscountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Prepayment Discount, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentPrepaymentDiscountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of discount received by the entity on prepayment of debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentPrepaymentDiscountNumberOfDaysEarlyPayment" xlink:label="cntm_DebtInstrumentPrepaymentDiscountNumberOfDaysEarlyPayment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentPrepaymentDiscountNumberOfDaysEarlyPayment" xlink:to="cntm_DebtInstrumentPrepaymentDiscountNumberOfDaysEarlyPayment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentPrepaymentDiscountNumberOfDaysEarlyPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of delays early payment for prepayment discount.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentPrepaymentDiscountNumberOfDaysEarlyPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Prepayment Discount, Number of Days Early Payment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentPrepaymentDiscountNumberOfDaysEarlyPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of days early payment of prepayment discount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BeneficialOwnershipPercentage" xlink:label="cntm_BeneficialOwnershipPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BeneficialOwnershipPercentage" xlink:to="cntm_BeneficialOwnershipPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BeneficialOwnershipPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of beneficial equity interest by an entity in the reporting entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BeneficialOwnershipPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beneficial Ownership Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BeneficialOwnershipPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of beneficial ownership</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentRedemptionPricePercentageOfPrepaymentPremium" xlink:label="cntm_DebtInstrumentRedemptionPricePercentageOfPrepaymentPremium" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRedemptionPricePercentageOfPrepaymentPremium" xlink:to="cntm_DebtInstrumentRedemptionPricePercentageOfPrepaymentPremium_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRedemptionPricePercentageOfPrepaymentPremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of prepayment premium payable on the principal amount of debt redeemed.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRedemptionPricePercentageOfPrepaymentPremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption Price, Percentage of Prepayment Premium</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRedemptionPricePercentageOfPrepaymentPremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of prepayment premium payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentRedemptionNoticePeriod" xlink:label="cntm_DebtInstrumentRedemptionNoticePeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRedemptionNoticePeriod" xlink:to="cntm_DebtInstrumentRedemptionNoticePeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRedemptionNoticePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The period of written notice to be provided by the entity before redemption of the debt instrument, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRedemptionNoticePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Notice Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRedemptionNoticePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption notice period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtRelatedCommitmentFees" xlink:label="cntm_DebtRelatedCommitmentFees" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtRelatedCommitmentFees" xlink:to="cntm_DebtRelatedCommitmentFees_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtRelatedCommitmentFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the charge against earnings during the period for commitment fees.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtRelatedCommitmentFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Related Commitment Fees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtRelatedCommitmentFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitment fees</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PaymentsOfUpfrontCommitmentFee" xlink:label="cntm_PaymentsOfUpfrontCommitmentFee" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentsOfUpfrontCommitmentFee" xlink:to="cntm_PaymentsOfUpfrontCommitmentFee_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentsOfUpfrontCommitmentFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of payments of upfront commitment fee related to debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentsOfUpfrontCommitmentFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments Of Upfront Commitment Fee</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PaymentsOfUpfrontCommitmentFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment of upfront commitment fees</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MaximumStockIssuableSharesConversionOfConvertibleSecurities" xlink:label="cntm_MaximumStockIssuableSharesConversionOfConvertibleSecurities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MaximumStockIssuableSharesConversionOfConvertibleSecurities" xlink:to="cntm_MaximumStockIssuableSharesConversionOfConvertibleSecurities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MaximumStockIssuableSharesConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum number of shares issuable as a result of conversion of convertible securities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MaximumStockIssuableSharesConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum Stock Issuable, Shares, Conversion of Convertible Securities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MaximumStockIssuableSharesConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum number of shares issuable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentEventOfDefaultCurePeriod" xlink:label="cntm_DebtInstrumentEventOfDefaultCurePeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentEventOfDefaultCurePeriod" xlink:to="cntm_DebtInstrumentEventOfDefaultCurePeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentEventOfDefaultCurePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of trading days allowed to cure an event of default under a debt instrument, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentEventOfDefaultCurePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Event Of Default, Cure Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentEventOfDefaultCurePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cure period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentEventOfDefaultUndismissedProceedingsCurePeriod" xlink:label="cntm_DebtInstrumentEventOfDefaultUndismissedProceedingsCurePeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentEventOfDefaultUndismissedProceedingsCurePeriod" xlink:to="cntm_DebtInstrumentEventOfDefaultUndismissedProceedingsCurePeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentEventOfDefaultUndismissedProceedingsCurePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of days specified in a debt agreement during which a bankruptcy or insolvency proceeding may remain undismissed before constituting an event of default, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentEventOfDefaultUndismissedProceedingsCurePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Event Of Default, Undismissed Proceedings, Cure Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentEventOfDefaultUndismissedProceedingsCurePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Undismissed proceedings, cure period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentOtherIndebtednessEventOfDefaultThresholdAmount" xlink:label="cntm_DebtInstrumentOtherIndebtednessEventOfDefaultThresholdAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentOtherIndebtednessEventOfDefaultThresholdAmount" xlink:to="cntm_DebtInstrumentOtherIndebtednessEventOfDefaultThresholdAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentOtherIndebtednessEventOfDefaultThresholdAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The threshold amount of other indebtedness that, if defaulted upon, triggers an event of default under a debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentOtherIndebtednessEventOfDefaultThresholdAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Other Indebtedness Event Of Default, Threshold Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentOtherIndebtednessEventOfDefaultThresholdAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold amount of other indebtedness</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentFinalJudgmentEventOfDefaultThresholdAmount" xlink:label="cntm_DebtInstrumentFinalJudgmentEventOfDefaultThresholdAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentFinalJudgmentEventOfDefaultThresholdAmount" xlink:to="cntm_DebtInstrumentFinalJudgmentEventOfDefaultThresholdAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentFinalJudgmentEventOfDefaultThresholdAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The aggregate threshold amount of final judgments against the company that, if exceeded and remaining unsatisfied for the specified period, constitutes an event of default under a debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentFinalJudgmentEventOfDefaultThresholdAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Final Judgment Event Of Default, Threshold Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentFinalJudgmentEventOfDefaultThresholdAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The aggregate threshold amount of final judgments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentFinalJudgmentEventOfDefaultUnsatisfiedPeriod" xlink:label="cntm_DebtInstrumentFinalJudgmentEventOfDefaultUnsatisfiedPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentFinalJudgmentEventOfDefaultUnsatisfiedPeriod" xlink:to="cntm_DebtInstrumentFinalJudgmentEventOfDefaultUnsatisfiedPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentFinalJudgmentEventOfDefaultUnsatisfiedPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Final Judgment Event Of Default, Unsatisfied Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentFinalJudgmentEventOfDefaultUnsatisfiedPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Final Judgment Event Of Default, Unsatisfied Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentFinalJudgmentEventOfDefaultUnsatisfiedPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Final judgement event of default, unsatisfied period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentCessationOfTradingEventOfDefaultPeriod" xlink:label="cntm_DebtInstrumentCessationOfTradingEventOfDefaultPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentCessationOfTradingEventOfDefaultPeriod" xlink:to="cntm_DebtInstrumentCessationOfTradingEventOfDefaultPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentCessationOfTradingEventOfDefaultPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of consecutive trading days during which the company's common stock may cease trading on its principal market before constituting an event of default under a debt instrument, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentCessationOfTradingEventOfDefaultPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Cessation Of Trading, Event Of Default Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentCessationOfTradingEventOfDefaultPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cessation of trading, event of default period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentOtherEventOfDefaultCurePeriod" xlink:label="cntm_DebtInstrumentOtherEventOfDefaultCurePeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentOtherEventOfDefaultCurePeriod" xlink:to="cntm_DebtInstrumentOtherEventOfDefaultCurePeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentOtherEventOfDefaultCurePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of trading days allowed to cure other material covenant event of default under a debt instrument, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentOtherEventOfDefaultCurePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Other Event Of Default, Cure Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentOtherEventOfDefaultCurePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other event of default, cure period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFinanceCostsNet" xlink:label="us-gaap_DeferredFinanceCostsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredFinanceCostsNet" xlink:to="us-gaap_DeferredFinanceCostsNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Issuance Costs, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred fee</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentTerminationFees" xlink:label="cntm_DebtInstrumentTerminationFees" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentTerminationFees" xlink:to="cntm_DebtInstrumentTerminationFees_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentTerminationFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount payable upon termination of a debt or equity line agreement, measured at fair value as of the termination date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentTerminationFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Termination Fees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentTerminationFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Termination fee</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentRightOfFirstRefusalPeriod" xlink:label="cntm_DebtInstrumentRightOfFirstRefusalPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRightOfFirstRefusalPeriod" xlink:to="cntm_DebtInstrumentRightOfFirstRefusalPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRightOfFirstRefusalPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The period during which a counterparty has the first right to provide an equity line of credit before the company can enter into such an arrangement with another party, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRightOfFirstRefusalPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Right Of First Refusal Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRightOfFirstRefusalPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right of first refusal period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentFinalRepayment" xlink:label="cntm_DebtInstrumentFinalRepayment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentFinalRepayment" xlink:to="cntm_DebtInstrumentFinalRepayment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentFinalRepayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of the final scheduled payment required to fully settle a debt obligation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentFinalRepayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Final Repayment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentFinalRepayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Final payment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2025IssuanceOneMember" xlink:label="cntm_ConvertibleNotes2025IssuanceOneMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2025IssuanceOneMember" xlink:to="cntm_ConvertibleNotes2025IssuanceOneMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2025IssuanceOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to first issuance of convertible notes 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2025IssuanceOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2025, Issuance One [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2025IssuanceOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">5/25/2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2025IssuanceTwoMember" xlink:label="cntm_ConvertibleNotes2025IssuanceTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2025IssuanceTwoMember" xlink:to="cntm_ConvertibleNotes2025IssuanceTwoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2025IssuanceTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to second issuance of convertible notes 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2025IssuanceTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2025, Issuance Two [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2025IssuanceTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">10/1/2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2025IssuanceThreeMember" xlink:label="cntm_ConvertibleNotes2025IssuanceThreeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2025IssuanceThreeMember" xlink:to="cntm_ConvertibleNotes2025IssuanceThreeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2025IssuanceThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to third issuance of convertible notes 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2025IssuanceThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2025, Issuance Three [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2025IssuanceThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">10/7/2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2025IssuanceFourMember" xlink:label="cntm_ConvertibleNotes2025IssuanceFourMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2025IssuanceFourMember" xlink:to="cntm_ConvertibleNotes2025IssuanceFourMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2025IssuanceFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to fourth issuance of convertible notes 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2025IssuanceFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2025, Issuance Four [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2025IssuanceFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">10/23/2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2025IssuanceFiveMember" xlink:label="cntm_ConvertibleNotes2025IssuanceFiveMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2025IssuanceFiveMember" xlink:to="cntm_ConvertibleNotes2025IssuanceFiveMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2025IssuanceFiveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to fifth issuance of convertible notes 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2025IssuanceFiveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2025, Issuance Five [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2025IssuanceFiveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">11/25/2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2025IssuanceSixMember" xlink:label="cntm_ConvertibleNotes2025IssuanceSixMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2025IssuanceSixMember" xlink:to="cntm_ConvertibleNotes2025IssuanceSixMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2025IssuanceSixMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Sixth issuance of convertible notes 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2025IssuanceSixMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2025, Issuance Six [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2025IssuanceSixMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">11/25/2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2025IssuanceSevenMember" xlink:label="cntm_ConvertibleNotes2025IssuanceSevenMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2025IssuanceSevenMember" xlink:to="cntm_ConvertibleNotes2025IssuanceSevenMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2025IssuanceSevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to seventh issuance of convertible notes 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2025IssuanceSevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2025, Issuance Seven [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2025IssuanceSevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">12/2/2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2025IssuanceEightMember" xlink:label="cntm_ConvertibleNotes2025IssuanceEightMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2025IssuanceEightMember" xlink:to="cntm_ConvertibleNotes2025IssuanceEightMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2025IssuanceEightMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to eighth issuance of convertible notes 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2025IssuanceEightMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2025, Issuance Eight [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2025IssuanceEightMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">12/8/2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2025IssuanceNineMember" xlink:label="cntm_ConvertibleNotes2025IssuanceNineMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2025IssuanceNineMember" xlink:to="cntm_ConvertibleNotes2025IssuanceNineMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2025IssuanceNineMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to ninth issuance of convertible notes 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2025IssuanceNineMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2025, Issuance Nine [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2025IssuanceNineMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">12/8/2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2025IssuanceTenMember" xlink:label="cntm_ConvertibleNotes2025IssuanceTenMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2025IssuanceTenMember" xlink:to="cntm_ConvertibleNotes2025IssuanceTenMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2025IssuanceTenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to tenth issuance of convertible notes 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2025IssuanceTenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2025, Issuance Ten [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2025IssuanceTenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">12/8/2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2025IssuanceElevenMember" xlink:label="cntm_ConvertibleNotes2025IssuanceElevenMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2025IssuanceElevenMember" xlink:to="cntm_ConvertibleNotes2025IssuanceElevenMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2025IssuanceElevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to eleventh issuance of convertible notes 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2025IssuanceElevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2025, Issuance Eleven [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2025IssuanceElevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">12/16/2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2026IssuanceOneMember" xlink:label="cntm_ConvertibleNotes2026IssuanceOneMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceOneMember" xlink:to="cntm_ConvertibleNotes2026IssuanceOneMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to first issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance One [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">1/1/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2026IssuanceTwoMember" xlink:label="cntm_ConvertibleNotes2026IssuanceTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceTwoMember" xlink:to="cntm_ConvertibleNotes2026IssuanceTwoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to second issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Two [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">1/7/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2026IssuanceThreeMember" xlink:label="cntm_ConvertibleNotes2026IssuanceThreeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceThreeMember" xlink:to="cntm_ConvertibleNotes2026IssuanceThreeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to third issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Three [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">1/13/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2026IssuanceFourMember" xlink:label="cntm_ConvertibleNotes2026IssuanceFourMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceFourMember" xlink:to="cntm_ConvertibleNotes2026IssuanceFourMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to fourth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Four [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">1/14/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2026IssuanceFiveMember" xlink:label="cntm_ConvertibleNotes2026IssuanceFiveMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceFiveMember" xlink:to="cntm_ConvertibleNotes2026IssuanceFiveMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceFiveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to fifth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceFiveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Five [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceFiveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">1/20/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2026IssuanceSixMember" xlink:label="cntm_ConvertibleNotes2026IssuanceSixMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceSixMember" xlink:to="cntm_ConvertibleNotes2026IssuanceSixMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceSixMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to sixth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceSixMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Six [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceSixMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">1/22/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2026IssuanceSevenMember" xlink:label="cntm_ConvertibleNotes2026IssuanceSevenMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceSevenMember" xlink:to="cntm_ConvertibleNotes2026IssuanceSevenMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceSevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to seventh issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceSevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Seven [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceSevenMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">1/27/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2026IssuanceEightMember" xlink:label="cntm_ConvertibleNotes2026IssuanceEightMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceEightMember" xlink:to="cntm_ConvertibleNotes2026IssuanceEightMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceEightMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to eighth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceEightMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Eight [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceEightMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2/12/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2026IssuanceNineMember" xlink:label="cntm_ConvertibleNotes2026IssuanceNineMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2026IssuanceNineMember" xlink:to="cntm_ConvertibleNotes2026IssuanceNineMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2026IssuanceNineMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to nineth issuance of convertible notes 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2026IssuanceNineMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2026, Issuance Nine [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2026IssuanceNineMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">3/30/2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConversionOptionPeriodFirst210DaysFollowingIssuanceOfConvertibleNoteMember" xlink:label="cntm_ConversionOptionPeriodFirst210DaysFollowingIssuanceOfConvertibleNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConversionOptionPeriodFirst210DaysFollowingIssuanceOfConvertibleNoteMember" xlink:to="cntm_ConversionOptionPeriodFirst210DaysFollowingIssuanceOfConvertibleNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConversionOptionPeriodFirst210DaysFollowingIssuanceOfConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to conversion option period being first 210 days following the issuance of convertible note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConversionOptionPeriodFirst210DaysFollowingIssuanceOfConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion Option Period, First 210 Days Following Issuance Of Convertible Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConversionOptionPeriodFirst210DaysFollowingIssuanceOfConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">First 210 days following issuance of convertible note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConversionOptionPeriod180DaysFollowingIssuanceOfConvertibleNoteMember" xlink:label="cntm_ConversionOptionPeriod180DaysFollowingIssuanceOfConvertibleNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConversionOptionPeriod180DaysFollowingIssuanceOfConvertibleNoteMember" xlink:to="cntm_ConversionOptionPeriod180DaysFollowingIssuanceOfConvertibleNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConversionOptionPeriod180DaysFollowingIssuanceOfConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to conversion option period being 180 days following the issuance of convertible note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConversionOptionPeriod180DaysFollowingIssuanceOfConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion Option Period, 180 Days Following Issuance Of Convertible Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConversionOptionPeriod180DaysFollowingIssuanceOfConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">180 days period after issuance of convertible note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentConvertibleTermFromIssuance" xlink:label="cntm_DebtInstrumentConvertibleTermFromIssuance" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConvertibleTermFromIssuance" xlink:to="cntm_DebtInstrumentConvertibleTermFromIssuance_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConvertibleTermFromIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the term for conversion of debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConvertibleTermFromIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Term from Issuance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_DebtInstrumentConvertibleTermFromIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion Option Period of Exercisability (from issuance date)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNoteConversionVolumeWeightedAveragePricePercentage" xlink:label="cntm_ConvertibleNoteConversionVolumeWeightedAveragePricePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNoteConversionVolumeWeightedAveragePricePercentage" xlink:to="cntm_ConvertibleNoteConversionVolumeWeightedAveragePricePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNoteConversionVolumeWeightedAveragePricePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of lowest daily volume weighted average price at which convertible note is converted into common shares.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNoteConversionVolumeWeightedAveragePricePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Note, Conversion, Volume Weighted Average Price, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNoteConversionVolumeWeightedAveragePricePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted average price, Percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentAverageTradingPriceNumberOfBusinessDays" xlink:label="cntm_DebtInstrumentAverageTradingPriceNumberOfBusinessDays" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentAverageTradingPriceNumberOfBusinessDays" xlink:to="cntm_DebtInstrumentAverageTradingPriceNumberOfBusinessDays_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentAverageTradingPriceNumberOfBusinessDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the number of business days immediately after the specified consecutive trading day period in which the average trading price was equal to or less than the specified percentage of the average conversion value of the note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentAverageTradingPriceNumberOfBusinessDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument Average Trading Price Number of Business Days</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentAverageTradingPriceNumberOfBusinessDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of trading days immediately prior to applicable measurement date</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNoteConversionNumberOfTradingDays" xlink:label="cntm_ConvertibleNoteConversionNumberOfTradingDays" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNoteConversionNumberOfTradingDays" xlink:to="cntm_ConvertibleNoteConversionNumberOfTradingDays_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNoteConversionNumberOfTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of trading days preceding which conversion of convertible note into common shares is calculated at volume weighted average price.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNoteConversionNumberOfTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Note, Conversion, Number of Trading Days</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNoteConversionNumberOfTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of trading days</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleDebtConversionPriceFloor" xlink:label="cntm_ConvertibleDebtConversionPriceFloor" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleDebtConversionPriceFloor" xlink:to="cntm_ConvertibleDebtConversionPriceFloor_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleDebtConversionPriceFloor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The minimum conversion price per share at which a convertible instrument may be converted into equity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleDebtConversionPriceFloor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Debt Conversion Price Floor</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleDebtConversionPriceFloor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion price, floor</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleDebtConversionPriceDiscountPercentage" xlink:label="cntm_ConvertibleDebtConversionPriceDiscountPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleDebtConversionPriceDiscountPercentage" xlink:to="cntm_ConvertibleDebtConversionPriceDiscountPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleDebtConversionPriceDiscountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage applied to the market price of the underlying equity to determine the conversion price.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleDebtConversionPriceDiscountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Debt Conversion Price Discount Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleDebtConversionPriceDiscountPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion price, discount percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNoteConversionVolumeWeightedAverageTradingPricePercentage" xlink:label="cntm_ConvertibleNoteConversionVolumeWeightedAverageTradingPricePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNoteConversionVolumeWeightedAverageTradingPricePercentage" xlink:to="cntm_ConvertibleNoteConversionVolumeWeightedAverageTradingPricePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNoteConversionVolumeWeightedAverageTradingPricePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of lowest daily volume weighted average trading price percentage at which convertible note is converted into common shares.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNoteConversionVolumeWeightedAverageTradingPricePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Note Conversion Volume Weighted Average Trading Price Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNoteConversionVolumeWeightedAverageTradingPricePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible note is convertible at a price</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SecuredPromissoryNoteMember" xlink:label="cntm_SecuredPromissoryNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SecuredPromissoryNoteMember" xlink:to="cntm_SecuredPromissoryNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SecuredPromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to secured promissory notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SecuredPromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Secured Promissory Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SecuredPromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Secured Promissory Notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SmalBusinessAdministrationLoansMember" xlink:label="cntm_SmalBusinessAdministrationLoansMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SmalBusinessAdministrationLoansMember" xlink:to="cntm_SmalBusinessAdministrationLoansMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SmalBusinessAdministrationLoansMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to small business administration loans.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SmalBusinessAdministrationLoansMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Smal Business Administration Loans [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SmalBusinessAdministrationLoansMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Small Business Administration Loans</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesPayableOtherPayablesMember" xlink:label="us-gaap_NotesPayableOtherPayablesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesPayableOtherPayablesMember" xlink:to="us-gaap_NotesPayableOtherPayablesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NotesPayableOtherPayablesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payable, Other Payables [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NotesPayableOtherPayablesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Promissory Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_VehicleNotesMember" xlink:label="cntm_VehicleNotesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_VehicleNotesMember" xlink:to="cntm_VehicleNotesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_VehicleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to vehicle notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_VehicleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vehicle Notes [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_VehicleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vehicle Notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SellerNotesMember" xlink:label="cntm_SellerNotesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SellerNotesMember" xlink:to="cntm_SellerNotesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SellerNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to seller notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SellerNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Seller Notes [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SellerNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Seller Notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AvantiNotesMember" xlink:label="cntm_AvantiNotesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AvantiNotesMember" xlink:to="cntm_AvantiNotesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AvantiNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to avanti notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AvantiNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Avanti Notes [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AvantiNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Avanti Notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_RealEstatePromissoryNoteMember" xlink:label="cntm_RealEstatePromissoryNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RealEstatePromissoryNoteMember" xlink:to="cntm_RealEstatePromissoryNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RealEstatePromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to real estate promissory note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RealEstatePromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Promissory Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RealEstatePromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Promissory Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessLoanAndSecurityAgreementMember" xlink:label="cntm_BusinessLoanAndSecurityAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessLoanAndSecurityAgreementMember" xlink:to="cntm_BusinessLoanAndSecurityAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessLoanAndSecurityAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to business loan and security agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessLoanAndSecurityAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Loan And Security Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessLoanAndSecurityAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Loan and Security Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SaleOfFutureReceiptsMember" xlink:label="cntm_SaleOfFutureReceiptsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SaleOfFutureReceiptsMember" xlink:to="cntm_SaleOfFutureReceiptsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SaleOfFutureReceiptsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the sale of future receipts.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SaleOfFutureReceiptsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale Of Future Receipts [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SaleOfFutureReceiptsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Future Receipts</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PurchaseOrderFinancingMember" xlink:label="cntm_PurchaseOrderFinancingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PurchaseOrderFinancingMember" xlink:to="cntm_PurchaseOrderFinancingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PurchaseOrderFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to purchase order financing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PurchaseOrderFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase Order Financing [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PurchaseOrderFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase Order Financing</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SaleOfFutureReceiptsLibertasMember" xlink:label="cntm_SaleOfFutureReceiptsLibertasMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SaleOfFutureReceiptsLibertasMember" xlink:to="cntm_SaleOfFutureReceiptsLibertasMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SaleOfFutureReceiptsLibertasMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to sale of future receipts - Libertas.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SaleOfFutureReceiptsLibertasMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Future Receipts - Libertas [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_SaleOfFutureReceiptsLibertasMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyMember" xlink:label="us-gaap_RelatedPartyMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyMember" xlink:to="us-gaap_RelatedPartyMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related party</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:to="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Unamortized Discount (Premium) and Debt Issuance Costs, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: debt discount and issuance costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: Debt discount and issuance costs</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NotesPayablesCurrent" xlink:label="cntm_NotesPayablesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NotesPayablesCurrent" xlink:to="cntm_NotesPayablesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NotesPayablesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sum of the carrying values as of the balance sheet date of the portions of long-term notes payable due within one year or the operating cycle if longer.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NotesPayablesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payables, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_NotesPayablesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: notes payable, current portion</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NotesPayablesNoncurrent" xlink:label="cntm_NotesPayablesNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NotesPayablesNoncurrent" xlink:to="cntm_NotesPayablesNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NotesPayablesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying value as of the balance sheet date of notes payable (with maturities initially due after one year or beyond the operating cycle if longer), excluding current portion.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NotesPayablesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payables, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NotesPayablesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt, net of current portion</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="cntm_NotesPayablesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes payable, net of debt issuance costs and current portion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseDebt" xlink:label="us-gaap_InterestExpenseDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestExpenseDebt" xlink:to="us-gaap_InterestExpenseDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestExpenseDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Expense, Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestExpenseDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest expense</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AccruedInterestOnDebt" xlink:label="cntm_AccruedInterestOnDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AccruedInterestOnDebt" xlink:to="cntm_AccruedInterestOnDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AccruedInterestOnDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of accrued interest on debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AccruedInterestOnDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued Interest On Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AccruedInterestOnDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of accrued interest on debt instrument</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesAxis" xlink:label="srt_ConsolidatedEntitiesAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ConsolidatedEntitiesAxis" xlink:to="srt_ConsolidatedEntitiesAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ConsolidatedEntitiesAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidated Entities [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesDomain" xlink:label="srt_ConsolidatedEntitiesDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ConsolidatedEntitiesDomain" xlink:to="srt_ConsolidatedEntitiesDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ConsolidatedEntitiesDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidated Entities [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentRedemptionPremiumPercentageOfOriginalPrincipalAmount" xlink:label="cntm_DebtInstrumentRedemptionPremiumPercentageOfOriginalPrincipalAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRedemptionPremiumPercentageOfOriginalPrincipalAmount" xlink:to="cntm_DebtInstrumentRedemptionPremiumPercentageOfOriginalPrincipalAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRedemptionPremiumPercentageOfOriginalPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption premium as a percentage of original principal amount.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRedemptionPremiumPercentageOfOriginalPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption Premium, Percentage of Original Principal Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRedemptionPremiumPercentageOfOriginalPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption premium as a percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FutureReceiptsSoldAndAssignedValue" xlink:label="cntm_FutureReceiptsSoldAndAssignedValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FutureReceiptsSoldAndAssignedValue" xlink:to="cntm_FutureReceiptsSoldAndAssignedValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FutureReceiptsSoldAndAssignedValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of Future Receipts sold and assigned by the company.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FutureReceiptsSoldAndAssignedValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Future Receipts Sold And Assigned Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FutureReceiptsSoldAndAssignedValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Company sold and assigned</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FeeReceivedForFutureReceiptsSoldAndAssigned" xlink:label="cntm_FeeReceivedForFutureReceiptsSoldAndAssigned" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FeeReceivedForFutureReceiptsSoldAndAssigned" xlink:to="cntm_FeeReceivedForFutureReceiptsSoldAndAssigned_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FeeReceivedForFutureReceiptsSoldAndAssigned_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of fees received from Future Receipts sold and assigned, pursuant to an agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FeeReceivedForFutureReceiptsSoldAndAssigned_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fee Received For Future Receipts Sold And Assigned</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FeeReceivedForFutureReceiptsSoldAndAssigned_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fee of future receipts</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentUnamortizedDiscount" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentUnamortizedDiscount" xlink:to="us-gaap_DebtInstrumentUnamortizedDiscount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Unamortized Discount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unamortized debt discount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MinimumWeeklySalesReceiptsAgreedToPay" xlink:label="cntm_MinimumWeeklySalesReceiptsAgreedToPay" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MinimumWeeklySalesReceiptsAgreedToPay" xlink:to="cntm_MinimumWeeklySalesReceiptsAgreedToPay_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MinimumWeeklySalesReceiptsAgreedToPay_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum amount of weekly sales receipts agreed to pay until the Future Receipts have been collected, pursuant to an agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MinimumWeeklySalesReceiptsAgreedToPay_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum Weekly Sales Receipts Agreed To Pay</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MinimumWeeklySalesReceiptsAgreedToPay_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum weekly sales receipts agreed to pay</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessLoanAndSecurityAgreementJanuary2026Member" xlink:label="cntm_BusinessLoanAndSecurityAgreementJanuary2026Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessLoanAndSecurityAgreementJanuary2026Member" xlink:to="cntm_BusinessLoanAndSecurityAgreementJanuary2026Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessLoanAndSecurityAgreementJanuary2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to the January 2026 business loan and security agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessLoanAndSecurityAgreementJanuary2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Loan And Security Agreement, January 2026 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessLoanAndSecurityAgreementJanuary2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">January 2026 Term Loan</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessLoanAndSecurityAgreementMarch2026Member" xlink:label="cntm_BusinessLoanAndSecurityAgreementMarch2026Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessLoanAndSecurityAgreementMarch2026Member" xlink:to="cntm_BusinessLoanAndSecurityAgreementMarch2026Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessLoanAndSecurityAgreementMarch2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to the March 2026 business loan and security agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessLoanAndSecurityAgreementMarch2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Loan And Security Agreement, March 2026 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessLoanAndSecurityAgreementMarch2026Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">March 2026 Term Loan</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentNumberOfPeriodicPayment" xlink:label="cntm_DebtInstrumentNumberOfPeriodicPayment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentNumberOfPeriodicPayment" xlink:to="cntm_DebtInstrumentNumberOfPeriodicPayment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentNumberOfPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of periodic payment for a debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentNumberOfPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Number of Periodic Payment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentNumberOfPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of periodic payment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentPeriodicPayment" xlink:label="us-gaap_DebtInstrumentPeriodicPayment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentPeriodicPayment" xlink:to="us-gaap_DebtInstrumentPeriodicPayment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Periodic Payment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Periodic payments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bi-weekly payment amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentAggregateOfPrincipalAndInterest" xlink:label="cntm_DebtInstrumentAggregateOfPrincipalAndInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentAggregateOfPrincipalAndInterest" xlink:to="cntm_DebtInstrumentAggregateOfPrincipalAndInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentAggregateOfPrincipalAndInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate amount of principal and interest of a debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentAggregateOfPrincipalAndInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Aggregate Of Principal And Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentAggregateOfPrincipalAndInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate amount of principal and interest</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FactoringArrangementPurchaseOrderAndAccountsReceivableFinancingMember" xlink:label="cntm_FactoringArrangementPurchaseOrderAndAccountsReceivableFinancingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FactoringArrangementPurchaseOrderAndAccountsReceivableFinancingMember" xlink:to="cntm_FactoringArrangementPurchaseOrderAndAccountsReceivableFinancingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FactoringArrangementPurchaseOrderAndAccountsReceivableFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining purchase order and accounts receivable financing under factoring and security agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FactoringArrangementPurchaseOrderAndAccountsReceivableFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Factoring Arrangement, Purchase Order And Accounts Receivable Financing [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FactoringArrangementPurchaseOrderAndAccountsReceivableFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">PO and AR financing</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FactoringArrangementPurchaseOrderFinancingMember" xlink:label="cntm_FactoringArrangementPurchaseOrderFinancingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FactoringArrangementPurchaseOrderFinancingMember" xlink:to="cntm_FactoringArrangementPurchaseOrderFinancingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FactoringArrangementPurchaseOrderFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining purchase order financing under factoring and security agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FactoringArrangementPurchaseOrderFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Factoring Arrangement, Purchase Order Financing [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FactoringArrangementPurchaseOrderFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">PO financing</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FactoringArrangementAccountsReceivableFinancingMember" xlink:label="cntm_FactoringArrangementAccountsReceivableFinancingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FactoringArrangementAccountsReceivableFinancingMember" xlink:to="cntm_FactoringArrangementAccountsReceivableFinancingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FactoringArrangementAccountsReceivableFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining accounts receivable financing under factoring and security agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FactoringArrangementAccountsReceivableFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Factoring Arrangement, Accounts Receivable Financing [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FactoringArrangementAccountsReceivableFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AR financing</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CountyComfortServicesLlcMember" xlink:label="cntm_CountyComfortServicesLlcMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CountyComfortServicesLlcMember" xlink:to="cntm_CountyComfortServicesLlcMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CountyComfortServicesLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to County Comfort Services, LLC.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CountyComfortServicesLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">County Comfort Services, LLC [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CountyComfortServicesLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CCS</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_KeenLabsOperationsIncMember" xlink:label="cntm_KeenLabsOperationsIncMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_KeenLabsOperationsIncMember" xlink:to="cntm_KeenLabsOperationsIncMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_KeenLabsOperationsIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Keen Labs Operations Inc.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_KeenLabsOperationsIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Keen Labs Operations Inc [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_KeenLabsOperationsIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Keen Labs Operations, Inc</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ChargeAfter30DaysMember" xlink:label="cntm_ChargeAfter30DaysMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ChargeAfter30DaysMember" xlink:to="cntm_ChargeAfter30DaysMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ChargeAfter30DaysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to a scenario specifying the charge rate for each additional 10 day period after 30 days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ChargeAfter30DaysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Charge, After 30 Days [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ChargeAfter30DaysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">After 30 days</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ChargeInvoicesOutstandingForMoreThan60DaysMember" xlink:label="cntm_ChargeInvoicesOutstandingForMoreThan60DaysMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ChargeInvoicesOutstandingForMoreThan60DaysMember" xlink:to="cntm_ChargeInvoicesOutstandingForMoreThan60DaysMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ChargeInvoicesOutstandingForMoreThan60DaysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to a scenario specifying invoices outstanding for more than 60 days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ChargeInvoicesOutstandingForMoreThan60DaysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Charge, Invoices Outstanding For More Than 60 Days [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ChargeInvoicesOutstandingForMoreThan60DaysMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Invoice outstanding for more than 60 days</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FinancingFacilityMaximumBorrowingCapacity" xlink:label="cntm_FinancingFacilityMaximumBorrowingCapacity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityMaximumBorrowingCapacity" xlink:to="cntm_FinancingFacilityMaximumBorrowingCapacity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityMaximumBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum borrowing capacity under receivable financing facility that could be borrowed by the entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityMaximumBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Maximum Borrowing Capacity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityMaximumBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum borrowing capacity</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FinancingFacilityMaximumAdvanceAsPercentageOfEligibleReceivables" xlink:label="cntm_FinancingFacilityMaximumAdvanceAsPercentageOfEligibleReceivables" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityMaximumAdvanceAsPercentageOfEligibleReceivables" xlink:to="cntm_FinancingFacilityMaximumAdvanceAsPercentageOfEligibleReceivables_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityMaximumAdvanceAsPercentageOfEligibleReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum percentage of receivables that could be borrowed under the financing facility by the entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityMaximumAdvanceAsPercentageOfEligibleReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Maximum Advance As Percentage Of Eligible Receivables</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityMaximumAdvanceAsPercentageOfEligibleReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum advance on eligible receivables, percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FinancingFacilityThresholdPeriodPostInvoiceDateConsideredForEligibleReceivables" xlink:label="cntm_FinancingFacilityThresholdPeriodPostInvoiceDateConsideredForEligibleReceivables" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityThresholdPeriodPostInvoiceDateConsideredForEligibleReceivables" xlink:to="cntm_FinancingFacilityThresholdPeriodPostInvoiceDateConsideredForEligibleReceivables_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityThresholdPeriodPostInvoiceDateConsideredForEligibleReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold period post invoice date is considered for determination of eligible receivables for advance under financing facility expressed in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityThresholdPeriodPostInvoiceDateConsideredForEligibleReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Threshold Period Post Invoice Date Considered For Eligible Receivables</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityThresholdPeriodPostInvoiceDateConsideredForEligibleReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Eligible receivables, threshold number of days post invoice</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FinancingFacilityBaseChargeRatePercentage" xlink:label="cntm_FinancingFacilityBaseChargeRatePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityBaseChargeRatePercentage" xlink:to="cntm_FinancingFacilityBaseChargeRatePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityBaseChargeRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base charge rate for funds borrowed under financing facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityBaseChargeRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Base Charge Rate, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityBaseChargeRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base charge rate</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FinancingFacilityBaseChargeRateInitialTerm" xlink:label="cntm_FinancingFacilityBaseChargeRateInitialTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityBaseChargeRateInitialTerm" xlink:to="cntm_FinancingFacilityBaseChargeRateInitialTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityBaseChargeRateInitialTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period considered for base charge rate under the financing facility expressed in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityBaseChargeRateInitialTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Base Charge Rate, Initial Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityBaseChargeRateInitialTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base charge rate, initial term</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FinancingFacilityAdditionalChargeRatePercentage" xlink:label="cntm_FinancingFacilityAdditionalChargeRatePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityAdditionalChargeRatePercentage" xlink:to="cntm_FinancingFacilityAdditionalChargeRatePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityAdditionalChargeRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional charge rate over the base rate for funds borrowed and outstanding after initial term under the financing facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityAdditionalChargeRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Additional Charge Rate, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityAdditionalChargeRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional charge rate</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FinancingFacilityAdditionalChargeRateThresholdAdditionalPeriod" xlink:label="cntm_FinancingFacilityAdditionalChargeRateThresholdAdditionalPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityAdditionalChargeRateThresholdAdditionalPeriod" xlink:to="cntm_FinancingFacilityAdditionalChargeRateThresholdAdditionalPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityAdditionalChargeRateThresholdAdditionalPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold each additional period considered in the determination of additional charge rate under the financing facility expressed in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityAdditionalChargeRateThresholdAdditionalPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Additional Charge Rate, Threshold Additional Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityAdditionalChargeRateThresholdAdditionalPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional charge rate, each additional period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FinancingFacilityOutstandingMinimumPastDuePeriod" xlink:label="cntm_FinancingFacilityOutstandingMinimumPastDuePeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityOutstandingMinimumPastDuePeriod" xlink:to="cntm_FinancingFacilityOutstandingMinimumPastDuePeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityOutstandingMinimumPastDuePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aged invoices minimum past due period taken for determination of additional charge under financing facility, expressed in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityOutstandingMinimumPastDuePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Outstanding, Minimum Past Due Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityOutstandingMinimumPastDuePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum past due period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FinancingFacilityMinimumAdditionalFeesPerInvoice" xlink:label="cntm_FinancingFacilityMinimumAdditionalFeesPerInvoice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityMinimumAdditionalFeesPerInvoice" xlink:to="cntm_FinancingFacilityMinimumAdditionalFeesPerInvoice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityMinimumAdditionalFeesPerInvoice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum additional fee charged per invoice for aged receivables under the financing facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityMinimumAdditionalFeesPerInvoice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Minimum Additional Fees Per Invoice</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityMinimumAdditionalFeesPerInvoice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum additional fee per invoice</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FinancingFacilityBaseChargeRateThresholdEachPeriodPostDisbursementTillVerification" xlink:label="cntm_FinancingFacilityBaseChargeRateThresholdEachPeriodPostDisbursementTillVerification" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityBaseChargeRateThresholdEachPeriodPostDisbursementTillVerification" xlink:to="cntm_FinancingFacilityBaseChargeRateThresholdEachPeriodPostDisbursementTillVerification_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityBaseChargeRateThresholdEachPeriodPostDisbursementTillVerification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold each period considered in the determination of base charge rate under the financing facility expressed in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityBaseChargeRateThresholdEachPeriodPostDisbursementTillVerification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Base Charge Rate, Threshold Each Period Post Disbursement Till Verification</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityBaseChargeRateThresholdEachPeriodPostDisbursementTillVerification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base charge rate, threshold period post invoice</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FinancingFacilityTerm" xlink:label="cntm_FinancingFacilityTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityTerm" xlink:to="cntm_FinancingFacilityTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term for which the financing facility agreement been entered expressed in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FinancingFacilityMinimumAnnualVolumeRequirementAsPercentageOfFacility" xlink:label="cntm_FinancingFacilityMinimumAnnualVolumeRequirementAsPercentageOfFacility" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityMinimumAnnualVolumeRequirementAsPercentageOfFacility" xlink:to="cntm_FinancingFacilityMinimumAnnualVolumeRequirementAsPercentageOfFacility_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityMinimumAnnualVolumeRequirementAsPercentageOfFacility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum annual volume requirement expressed as percentage of facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityMinimumAnnualVolumeRequirementAsPercentageOfFacility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Minimum Annual Volume Requirement As Percentage Of Facility</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityMinimumAnnualVolumeRequirementAsPercentageOfFacility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum annual volume requirement, percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProceedsFromFinancingFacility" xlink:label="cntm_ProceedsFromFinancingFacility" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromFinancingFacility" xlink:to="cntm_ProceedsFromFinancingFacility_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromFinancingFacility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash inflow from the financing facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromFinancingFacility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Financing Facility</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsFromFinancingFacility_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advance received</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfPurchaseOrdersFinanced" xlink:label="cntm_NumberOfPurchaseOrdersFinanced" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfPurchaseOrdersFinanced" xlink:to="cntm_NumberOfPurchaseOrdersFinanced_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfPurchaseOrdersFinanced_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of purchase orders financed.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfPurchaseOrdersFinanced_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Purchase Orders Financed</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfPurchaseOrdersFinanced_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of purchase orders financed</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Recurring and Nonrecurring [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementFrequencyAxis" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByMeasurementFrequencyAxis" xlink:to="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Frequency [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementFrequencyDomain" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementFrequencyDomain" xlink:to="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Frequency [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsRecurringMember" xlink:label="us-gaap_FairValueMeasurementsRecurringMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementsRecurringMember" xlink:to="us-gaap_FairValueMeasurementsRecurringMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Recurring [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recurring</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Hierarchy and NAV [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Hierarchy and NAV [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member" xlink:label="us-gaap_FairValueInputsLevel3Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueInputsLevel3Member" xlink:to="us-gaap_FairValueInputsLevel3Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Inputs, Level 3 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Level 3</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">FAIR VALUE MEASUREMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosureAbstract" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="us-gaap_AssetsFairValueDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets, Fair Value Disclosure [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssets" xlink:label="us-gaap_DerivativeAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeAssets" xlink:to="us-gaap_DerivativeAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Asset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Forward purchase agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosure" xlink:label="us-gaap_AssetsFairValueDisclosure" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsFairValueDisclosure" xlink:to="us-gaap_AssetsFairValueDisclosure_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets, Fair Value Disclosure</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:label="us-gaap_LiabilitiesFairValueDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:to="us-gaap_LiabilitiesFairValueDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesFairValueDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities, Fair Value Disclosure [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesFairValueDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilities" xlink:label="us-gaap_DerivativeLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeLiabilities" xlink:to="us-gaap_DerivativeLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest expense</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationContingentConsiderationLiabilityFairValueDisclosure" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityFairValueDisclosure" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationContingentConsiderationLiabilityFairValueDisclosure" xlink:to="cntm_BusinessCombinationContingentConsiderationLiabilityFairValueDisclosure_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value portion of liability  recognized arising from contingent consideration in a business combination</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Liability, Fair Value Disclosure</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesFairValueDisclosure" xlink:label="us-gaap_LiabilitiesFairValueDisclosure" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesFairValueDisclosure" xlink:to="us-gaap_LiabilitiesFairValueDisclosure_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities, Fair Value Disclosure</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByAssetClassAxis" xlink:label="us-gaap_FairValueByAssetClassAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByAssetClassAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Class [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Class [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeFinancialInstrumentsAssetsMember" xlink:label="us-gaap_DerivativeFinancialInstrumentsAssetsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeFinancialInstrumentsAssetsMember" xlink:to="us-gaap_DerivativeFinancialInstrumentsAssetsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeFinancialInstrumentsAssetsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Financial Instruments, Assets [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeFinancialInstrumentsAssetsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Forward purchase agreement</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:to="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Financial Instruments, Liabilities [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationContingentConsiderationLiabilityMember" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationContingentConsiderationLiabilityMember" xlink:to="cntm_BusinessCombinationContingentConsiderationLiabilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to business combination contingent consideration liability.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Liability [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationContingentConsiderationLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value, assets measured on recurring basis</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:to="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTermination" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTermination" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTermination" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTermination_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of proceeds received on termination of financial instrument classified as an asset measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Termination</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash payment/(receipt)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetIssues" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetIssues" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetIssues" xlink:to="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetIssues_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Issuances</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuances</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:to="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Purchases</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement through issuance of Company's common stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement through issuance of Company's common stock and other adjustment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value, liabilities measured on recurring basis</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:to="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodEndLabel" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodStartLabel" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsCashPaid" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsCashPaid" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsCashPaid" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsCashPaid_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsCashPaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of settlement by cash of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsCashPaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Settlements, Cash Paid</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsCashPaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash payment/(receipt)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xlink:to="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Issuances</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuances</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityCommitmentSharesIssued" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityCommitmentSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityCommitmentSharesIssued" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityCommitmentSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityCommitmentSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of issuances of financial instrument classified as a liability measured using Commitment shares issued about the assumptions market participants would use in pricing</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityCommitmentSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Measurement With Unobservable Inputs Reconciliation Recurring Basis Liability Commitment shares issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityCommitmentSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitment shares issued</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsStockIssued" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsStockIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsStockIssued" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsStockIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of settlement by issuance of stock of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnIssuanceOfFinancialInstruments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain (loss) on issuance of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnIssuanceOfFinancialInstruments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Gain (Loss) On Issuance of Financial Instruments</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisReclassification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Reclassification</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisReclassification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Reclassification</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisReclassification_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclass from level 3</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAdditionalSettlementObligation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAdditionalSettlementObligation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAdditionalSettlementObligation" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAdditionalSettlementObligation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAdditionalSettlementObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of additional settlement of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAdditionalSettlementObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Additional Settlement Obligation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAdditionalSettlementObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional RJZ settlement amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByBalanceSheetGroupingTable" xlink:label="us-gaap_FairValueByBalanceSheetGroupingTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByBalanceSheetGroupingTable" xlink:to="us-gaap_FairValueByBalanceSheetGroupingTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByBalanceSheetGroupingTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, by Balance Sheet Grouping [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">FAIR VALUE MEASUREMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentAxis" xlink:label="us-gaap_FinancialInstrumentAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinancialInstrumentAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financial Instrument [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:label="us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputTypeAxis" xlink:label="us-gaap_MeasurementInputTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputDiscountRateMember" xlink:label="us-gaap_MeasurementInputDiscountRateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MeasurementInputDiscountRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Discount rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_MeasurementInputDiscountRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Discount Rate</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputProbabilityOfConversionAtMaturityScenarioMember" xlink:label="cntm_MeasurementInputProbabilityOfConversionAtMaturityScenarioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputProbabilityOfConversionAtMaturityScenarioMember" xlink:to="cntm_MeasurementInputProbabilityOfConversionAtMaturityScenarioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputProbabilityOfConversionAtMaturityScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using probability of conversion at maturity scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputProbabilityOfConversionAtMaturityScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Probability Of Conversion At Maturity Scenario [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputProbabilityOfConversionAtMaturityScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Probability of conversion at maturity scenario</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember" xlink:label="cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using probability of voluntary conversion scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Probability Of Voluntary Conversion Scenario [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Probability of voluntary conversion scenario/event of default scenarios</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Probability of voluntary conversion scenario</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputRemainingTermForConversionAtMaturityScenarioMember" xlink:label="cntm_MeasurementInputRemainingTermForConversionAtMaturityScenarioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputRemainingTermForConversionAtMaturityScenarioMember" xlink:to="cntm_MeasurementInputRemainingTermForConversionAtMaturityScenarioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputRemainingTermForConversionAtMaturityScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using remaining term for conversion at maturity scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputRemainingTermForConversionAtMaturityScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Remaining Term For Conversion At Maturity Scenario [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputRemainingTermForConversionAtMaturityScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining term for conversion at maturity scenario/event of default scenarios</label>
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    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputRemainingTermForVoluntaryConversionScenarioMember" xlink:label="cntm_MeasurementInputRemainingTermForVoluntaryConversionScenarioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputRemainingTermForVoluntaryConversionScenarioMember" xlink:to="cntm_MeasurementInputRemainingTermForVoluntaryConversionScenarioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">FAIR VALUE MEASUREMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentMeasurementInput" xlink:label="us-gaap_DebtInstrumentMeasurementInput" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentMeasurementInput" xlink:to="us-gaap_DebtInstrumentMeasurementInput_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Measurement Input</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value measurement input</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputDiscountRateIceBofaCccAndLowerUsHighYieldIndexMember" xlink:label="cntm_MeasurementInputDiscountRateIceBofaCccAndLowerUsHighYieldIndexMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputDiscountRateIceBofaCccAndLowerUsHighYieldIndexMember" xlink:to="cntm_MeasurementInputDiscountRateIceBofaCccAndLowerUsHighYieldIndexMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputDiscountRateIceBofaCccAndLowerUsHighYieldIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using interest rate relating to ICE BofA CCC &amp; Lower US High Yield Index to determine present value of future cash flows.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputDiscountRateIceBofaCccAndLowerUsHighYieldIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Discount Rate, Ice Bofa Ccc And Lower Us High Yield Index [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputDiscountRateIceBofaCccAndLowerUsHighYieldIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ICE BofA CCC &amp; Lower US High Yield Index</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputDiscountRateSAndPUsHighYieldCorporateBondCccIndexMember" xlink:label="cntm_MeasurementInputDiscountRateSAndPUsHighYieldCorporateBondCccIndexMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputDiscountRateSAndPUsHighYieldCorporateBondCccIndexMember" xlink:to="cntm_MeasurementInputDiscountRateSAndPUsHighYieldCorporateBondCccIndexMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputDiscountRateSAndPUsHighYieldCorporateBondCccIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using interest rate relating to the S&amp;P U.S. High Yield Corporate Bond CCC index  to determine present value of future cash flows.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputDiscountRateSAndPUsHighYieldCorporateBondCccIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Discount Rate, S And P Us High Yield Corporate Bond Ccc Index [Member</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputDiscountRateSAndPUsHighYieldCorporateBondCccIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S&amp;P U.S. High Yield Corporate Bond CCC index</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputDiscountRatePepperdinePrivateCapitalMarketsMezzanineRateOfReturnMember" xlink:label="cntm_MeasurementInputDiscountRatePepperdinePrivateCapitalMarketsMezzanineRateOfReturnMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputDiscountRatePepperdinePrivateCapitalMarketsMezzanineRateOfReturnMember" xlink:to="cntm_MeasurementInputDiscountRatePepperdinePrivateCapitalMarketsMezzanineRateOfReturnMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputDiscountRatePepperdinePrivateCapitalMarketsMezzanineRateOfReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using interest rate relating to the Pepperdine Private Capital Markets mezzanine required rate of return to determine present value of future cash flows.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputDiscountRatePepperdinePrivateCapitalMarketsMezzanineRateOfReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Discount Rate, Pepperdine Private Capital Markets Mezzanine Rate Of Return [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputDiscountRatePepperdinePrivateCapitalMarketsMezzanineRateOfReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Pepperdine Private Capital Markets mezzanine required rate of return</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCarryingAmount" xlink:label="us-gaap_DebtInstrumentCarryingAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentCarryingAmount" xlink:to="us-gaap_DebtInstrumentCarryingAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding balance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleDebtFairValueBeforeTermination" xlink:label="cntm_ConvertibleDebtFairValueBeforeTermination" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleDebtFairValueBeforeTermination" xlink:to="cntm_ConvertibleDebtFairValueBeforeTermination_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleDebtFairValueBeforeTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value portion of convertible debt before settlement and termination agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleDebtFairValueBeforeTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Debt, Fair Value Before Termination</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleDebtFairValueBeforeTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of outstanding balance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentTerminationFeePayable" xlink:label="cntm_DebtInstrumentTerminationFeePayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentTerminationFeePayable" xlink:to="cntm_DebtInstrumentTerminationFeePayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentTerminationFeePayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of termination fee payable in common stock for settlement of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentTerminationFeePayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Termination Fee Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentTerminationFeePayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Termination fee (payable in Common Stock at IPO price)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueOfTerminatedAgreement" xlink:label="cntm_FairValueOfTerminatedAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueOfTerminatedAgreement" xlink:to="cntm_FairValueOfTerminatedAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueOfTerminatedAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The fair value amount of the terminated agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueOfTerminatedAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Of Terminated Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueOfTerminatedAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value Of terminated agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BaseCaseScenarioMember" xlink:label="cntm_BaseCaseScenarioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BaseCaseScenarioMember" xlink:to="cntm_BaseCaseScenarioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BaseCaseScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to base case scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BaseCaseScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base Case Scenario [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BaseCaseScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base case scenario</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DefaultScenarioMember" xlink:label="cntm_DefaultScenarioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DefaultScenarioMember" xlink:to="cntm_DefaultScenarioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DefaultScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to default scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DefaultScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Default Scenario [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DefaultScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Default scenario</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputSharePriceMember" xlink:label="us-gaap_MeasurementInputSharePriceMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MeasurementInputSharePriceMember" xlink:to="us-gaap_MeasurementInputSharePriceMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MeasurementInputSharePriceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Share Price [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MeasurementInputSharePriceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_MeasurementInputSharePriceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock price as of valuation date</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputEquityVolatilityMember" xlink:label="cntm_MeasurementInputEquityVolatilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputEquityVolatilityMember" xlink:to="cntm_MeasurementInputEquityVolatilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputEquityVolatilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using equity volatility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputEquityVolatilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Equity Volatility [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputEquityVolatilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity volatility</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:label="us-gaap_MeasurementInputRiskFreeInterestRateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:to="us-gaap_MeasurementInputRiskFreeInterestRateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MeasurementInputRiskFreeInterestRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Risk Free Interest Rate [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MeasurementInputRiskFreeInterestRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Risk-free interest rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_MeasurementInputRiskFreeInterestRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Risk-free rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputExpectedTermMember" xlink:label="us-gaap_MeasurementInputExpectedTermMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MeasurementInputExpectedTermMember" xlink:to="us-gaap_MeasurementInputExpectedTermMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MeasurementInputExpectedTermMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Expected Term [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MeasurementInputExpectedTermMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expected term (in years)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_MeasurementInputExpectedTermMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expected term</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputDriftTermMember" xlink:label="cntm_MeasurementInputDriftTermMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputDriftTermMember" xlink:to="cntm_MeasurementInputDriftTermMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputDriftTermMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using drift term.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputDriftTermMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Drift Term [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputDriftTermMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Drift term</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_OtherLiabilitiesAgreedToBeSettledInShares" xlink:label="cntm_OtherLiabilitiesAgreedToBeSettledInShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_OtherLiabilitiesAgreedToBeSettledInShares" xlink:to="cntm_OtherLiabilitiesAgreedToBeSettledInShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_OtherLiabilitiesAgreedToBeSettledInShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of other liabilities settled through shares in non-cash transactions.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OtherLiabilitiesAgreedToBeSettledInShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Liabilities Agreed To Be Settled In Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_OtherLiabilitiesAgreedToBeSettledInShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Overdue liabilities agreed to be settled in shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SettlementAgreementFairValueAdjustment" xlink:label="cntm_SettlementAgreementFairValueAdjustment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementAgreementFairValueAdjustment" xlink:to="cntm_SettlementAgreementFairValueAdjustment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAgreementFairValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expense (income) related to adjustment to fair value of settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementAgreementFairValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Agreement, Fair Value Adjustment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAgreementFairValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfTrials" xlink:label="cntm_NumberOfTrials" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfTrials" xlink:to="cntm_NumberOfTrials_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfTrials_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the number of trials under a scenario-based framework.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfTrials_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Trials</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfTrials_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of trials</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BaseCaseScenarioProbabilityPercentage" xlink:label="cntm_BaseCaseScenarioProbabilityPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BaseCaseScenarioProbabilityPercentage" xlink:to="cntm_BaseCaseScenarioProbabilityPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BaseCaseScenarioProbabilityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of base case scenario probability.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BaseCaseScenarioProbabilityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base Case Scenario Probability, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BaseCaseScenarioProbabilityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base case scenario probability (in percent)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PercentageOfMarketPriceUsedToDetermineConversionPrice" xlink:label="cntm_PercentageOfMarketPriceUsedToDetermineConversionPrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PercentageOfMarketPriceUsedToDetermineConversionPrice" xlink:to="cntm_PercentageOfMarketPriceUsedToDetermineConversionPrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PercentageOfMarketPriceUsedToDetermineConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of market price used to determine conversion price.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PercentageOfMarketPriceUsedToDetermineConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage Of Market Price Used To Determine Conversion Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PercentageOfMarketPriceUsedToDetermineConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of market price used to determine conversion price</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DefaultScenarioProbabilityPercentage" xlink:label="cntm_DefaultScenarioProbabilityPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DefaultScenarioProbabilityPercentage" xlink:to="cntm_DefaultScenarioProbabilityPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DefaultScenarioProbabilityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of base case scenario probability.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DefaultScenarioProbabilityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Default Scenario Probability, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DefaultScenarioProbabilityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Default scenario probability (in percent)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SettlementAgreementMeasurementInput" xlink:label="cntm_SettlementAgreementMeasurementInput" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementAgreementMeasurementInput" xlink:to="cntm_SettlementAgreementMeasurementInput_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAgreementMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of input used to measure settlement agreement for shares issued under Section 3(a)(10) of the Securities Act.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementAgreementMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Agreement, Measurement Input</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAgreementMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Table]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MontereyCapitalAcquisitionCorporationMember" xlink:label="cntm_MontereyCapitalAcquisitionCorporationMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MontereyCapitalAcquisitionCorporationMember" xlink:to="cntm_MontereyCapitalAcquisitionCorporationMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MontereyCapitalAcquisitionCorporationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Monterey Capital Acquisition Corporation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MontereyCapitalAcquisitionCorporationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Monterey Capital Acquisition Corporation [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MontereyCapitalAcquisitionCorporationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Monterey Capital Acquisition Corporation</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SponsorMember" xlink:label="cntm_SponsorMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SponsorMember" xlink:to="cntm_SponsorMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SponsorMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">This member stands for sponsor.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SponsorMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sponsor [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SponsorMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sponsor</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_UnsecuredPromissoryNoteMember" xlink:label="cntm_UnsecuredPromissoryNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_UnsecuredPromissoryNoteMember" xlink:to="cntm_UnsecuredPromissoryNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_UnsecuredPromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to unsecured promissory note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_UnsecuredPromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unsecured Promissory Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_UnsecuredPromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unsecured promissory note</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems" xlink:label="us-gaap_RelatedPartyTransactionLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_RelatedPartyTransactionLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">RELATED PARTY TRANSACTIONS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt" xlink:to="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Liabilities, Long-Term Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unsecured promissory notes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:to="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Assets, Receivables</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AggregateOwnershipPercentageOfIndividualLenderMaximum" xlink:label="cntm_AggregateOwnershipPercentageOfIndividualLenderMaximum" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AggregateOwnershipPercentageOfIndividualLenderMaximum" xlink:to="cntm_AggregateOwnershipPercentageOfIndividualLenderMaximum_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AggregateOwnershipPercentageOfIndividualLenderMaximum_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The maximum percentage of ownership by an individual lender as per the terms of debt conversion.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AggregateOwnershipPercentageOfIndividualLenderMaximum_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate Ownership Percentage Of Individual Lender, Maximum</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AggregateOwnershipPercentageOfIndividualLenderMaximum_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum percentage of ownership by an individual lender</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ExtinguishmentOfDebtAmount" xlink:label="us-gaap_ExtinguishmentOfDebtAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ExtinguishmentOfDebtAmount" xlink:to="us-gaap_ExtinguishmentOfDebtAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ExtinguishmentOfDebtAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of Debt, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ExtinguishmentOfDebtAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ExtinguishmentOfAccountsPayableAndAccruedExpensesAmount" xlink:label="cntm_ExtinguishmentOfAccountsPayableAndAccruedExpensesAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ExtinguishmentOfAccountsPayableAndAccruedExpensesAmount" xlink:to="cntm_ExtinguishmentOfAccountsPayableAndAccruedExpensesAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ExtinguishmentOfAccountsPayableAndAccruedExpensesAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The total amount of accounts payable and accrued expenses extinguished by the entity during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ExtinguishmentOfAccountsPayableAndAccruedExpensesAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment Of Accounts Payable And Accrued Expenses, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ExtinguishmentOfAccountsPayableAndAccruedExpensesAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of accounts payable and accrued expenses</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PromissoryNote2016Member" xlink:label="cntm_PromissoryNote2016Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PromissoryNote2016Member" xlink:to="cntm_PromissoryNote2016Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PromissoryNote2016Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the 2016 promissory note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PromissoryNote2016Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Promissory Note 2016 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PromissoryNote2016Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2016 Promissory Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PromissoryNote2024Member" xlink:label="cntm_PromissoryNote2024Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PromissoryNote2024Member" xlink:to="cntm_PromissoryNote2024Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PromissoryNote2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the 2024 promissory note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PromissoryNote2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Promissory Note 2024 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PromissoryNote2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2024 Promissory Note</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ChiefExecutiveOfficerMember" xlink:label="srt_ChiefExecutiveOfficerMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ChiefExecutiveOfficerMember" xlink:to="srt_ChiefExecutiveOfficerMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ChiefExecutiveOfficerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chief Executive Officer [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ChiefExecutiveOfficerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chief executive officer</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFinancialLiabilities" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFinancialLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFinancialLiabilities" xlink:to="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFinancialLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFinancialLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Liability Assumed, Financial Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFinancialLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes acquired</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DistributedEnergyAndRenewablesMember" xlink:label="cntm_DistributedEnergyAndRenewablesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DistributedEnergyAndRenewablesMember" xlink:to="cntm_DistributedEnergyAndRenewablesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DistributedEnergyAndRenewablesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to distributed energy and renewables segment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DistributedEnergyAndRenewablesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributed Energy and Renewables [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DistributedEnergyAndRenewablesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributed Energy &amp; Renewables</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NonEmployeeDirectorMember" xlink:label="cntm_NonEmployeeDirectorMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NonEmployeeDirectorMember" xlink:to="cntm_NonEmployeeDirectorMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NonEmployeeDirectorMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to non-employee director.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NonEmployeeDirectorMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non Employee Director [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NonEmployeeDirectorMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-employee directors</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PeriodOfNoticeForTermination" xlink:label="cntm_PeriodOfNoticeForTermination" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PeriodOfNoticeForTermination" xlink:to="cntm_PeriodOfNoticeForTermination_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PeriodOfNoticeForTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period of notice for termination by either parties.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PeriodOfNoticeForTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period Of Notice For Termination</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MarkupOnTotalCostPercentage" xlink:label="cntm_MarkupOnTotalCostPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MarkupOnTotalCostPercentage" xlink:to="cntm_MarkupOnTotalCostPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MarkupOnTotalCostPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of mark up applied to total cost, including product cost, procurement and logistics fees, and marketing and other professional service costs.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MarkupOnTotalCostPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Markup On Total Cost, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MarkupOnTotalCostPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mark-up percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_IntraEntityGrossProfitInInventory" xlink:label="cntm_IntraEntityGrossProfitInInventory" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IntraEntityGrossProfitInInventory" xlink:to="cntm_IntraEntityGrossProfitInInventory_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IntraEntityGrossProfitInInventory_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of intra-entity gross profit remaining in inventory.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IntraEntityGrossProfitInInventory_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intra-Entity Gross Profit In Inventory</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross" xlink:to="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Restricted Stock Award, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Company issued restricted common stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllocatedShareBasedCompensationExpense" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllocatedShareBasedCompensationExpense" xlink:to="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-based compensation expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock-based compensation expense</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CommitmentsAndContingenciesTable" xlink:label="cntm_CommitmentsAndContingenciesTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommitmentsAndContingenciesTable" xlink:to="cntm_CommitmentsAndContingenciesTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommitmentsAndContingenciesTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule reflecting a Commitments and Contingencies.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommitmentsAndContingenciesTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">COMMITMENTS AND CONTINGENCIES [Table]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CommitmentsAndContingenciesLineItems" xlink:label="cntm_CommitmentsAndContingenciesLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommitmentsAndContingenciesLineItems" xlink:to="cntm_CommitmentsAndContingenciesLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommitmentsAndContingenciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommitmentsAndContingenciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments and Contingencies [Line items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CommitmentsAndContingenciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">COMMITMENTS AND CONTINGENCIES</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LossContingencyMortgageAndPromissoryNote" xlink:label="cntm_LossContingencyMortgageAndPromissoryNote" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LossContingencyMortgageAndPromissoryNote" xlink:to="cntm_LossContingencyMortgageAndPromissoryNote_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LossContingencyMortgageAndPromissoryNote_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated liability for a loss contingency arising from claims related to a mortgage and promissory note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LossContingencyMortgageAndPromissoryNote_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss Contingency, Mortgage And Promissory Note</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LossContingencyMortgageAndPromissoryNote_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mortgage and promissory note payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LossContingencyStockPurchaseAgreement" xlink:label="cntm_LossContingencyStockPurchaseAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LossContingencyStockPurchaseAgreement" xlink:to="cntm_LossContingencyStockPurchaseAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LossContingencyStockPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated liability for a loss contingency arising from claims related to stock purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LossContingencyStockPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss Contingency, Stock Purchase Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LossContingencyStockPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Damages relating to additional claims</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AttorneysFeesAndCosts" xlink:label="cntm_AttorneysFeesAndCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AttorneysFeesAndCosts" xlink:to="cntm_AttorneysFeesAndCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AttorneysFeesAndCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of attorney's fees and costs incurred.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AttorneysFeesAndCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Attorneys Fees And Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AttorneysFeesAndCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Attorneys' fees and costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_AttorneysFeesAndCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Attorneys' fees and costs</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ArbitratorsFeesAndCosts" xlink:label="cntm_ArbitratorsFeesAndCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ArbitratorsFeesAndCosts" xlink:to="cntm_ArbitratorsFeesAndCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ArbitratorsFeesAndCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of arbitrator's fees and costs incurred.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ArbitratorsFeesAndCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Arbitrators Fees And Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ArbitratorsFeesAndCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Arbitrators' fees and costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_ArbitratorsFeesAndCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Arbitrators' fees and costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingencyAccrualAtCarryingValue" xlink:label="us-gaap_LossContingencyAccrualAtCarryingValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LossContingencyAccrualAtCarryingValue" xlink:to="us-gaap_LossContingencyAccrualAtCarryingValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LossContingencyAccrualAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss Contingency Accrual</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LossContingencyAccrualAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss contingency accrual</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LitigationReserve" xlink:label="us-gaap_LitigationReserve" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LitigationReserve" xlink:to="us-gaap_LitigationReserve_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LitigationReserve_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated Litigation Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LitigationReserve_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Litigation reserve</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingencyDamagesSoughtValue" xlink:label="us-gaap_LossContingencyDamagesSoughtValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LossContingencyDamagesSoughtValue" xlink:to="us-gaap_LossContingencyDamagesSoughtValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LossContingencyDamagesSoughtValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss Contingency, Damages Sought, Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LossContingencyDamagesSoughtValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Obligation payments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtConversionConversionPrice" xlink:label="cntm_DebtConversionConversionPrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtConversionConversionPrice" xlink:to="cntm_DebtConversionConversionPrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtConversionConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Price per share for the conversion of debt into equity with equity shares divided by debt amount.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtConversionConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Conversion, Conversion Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtConversionConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion price</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ThresholdOwnershipPercentageForVendor" xlink:label="cntm_ThresholdOwnershipPercentageForVendor" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ThresholdOwnershipPercentageForVendor" xlink:to="cntm_ThresholdOwnershipPercentageForVendor_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ThresholdOwnershipPercentageForVendor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The maximum ownership interest of the company that allowed to be obtained by vendors.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ThresholdOwnershipPercentageForVendor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold Ownership Percentage For Vendor</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ThresholdOwnershipPercentageForVendor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold ownership percentage for vendor</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AdvisoryAgreementAmountPayable" xlink:label="cntm_AdvisoryAgreementAmountPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AdvisoryAgreementAmountPayable" xlink:to="cntm_AdvisoryAgreementAmountPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AdvisoryAgreementAmountPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount payable under advisory agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AdvisoryAgreementAmountPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advisory Agreement, Amount Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AdvisoryAgreementAmountPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount payable under advisory agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AdvisoryAgreementCashPaid" xlink:label="cntm_AdvisoryAgreementCashPaid" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AdvisoryAgreementCashPaid" xlink:to="cntm_AdvisoryAgreementCashPaid_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AdvisoryAgreementCashPaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash paid under advisory agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AdvisoryAgreementCashPaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advisory Agreement, Cash Paid</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AdvisoryAgreementCashPaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total cash payments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AdvisoryAgreementPayableInCash" xlink:label="cntm_AdvisoryAgreementPayableInCash" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AdvisoryAgreementPayableInCash" xlink:to="cntm_AdvisoryAgreementPayableInCash_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AdvisoryAgreementPayableInCash_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount to be paid in cash under advisory agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AdvisoryAgreementPayableInCash_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advisory Agreement, Payable In Cash</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AdvisoryAgreementPayableInCash_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advisory agreement, total cash payments for the unpaid balance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AdvisoryAgreementPayableByShares" xlink:label="cntm_AdvisoryAgreementPayableByShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AdvisoryAgreementPayableByShares" xlink:to="cntm_AdvisoryAgreementPayableByShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AdvisoryAgreementPayableByShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of shares to be issued under advisory agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AdvisoryAgreementPayableByShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advisory Agreement, Payable By Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AdvisoryAgreementPayableByShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advisory agreement, shares issued</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:to="us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments to Additional Paid in Capital, Stock Issued, Issuance Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional paid in capital</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Initial consideration of additional paid-in capital</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent" xlink:label="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent" xlink:to="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Defined Contribution Plan, Maximum Annual Contributions Per Employee, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of employee contribution</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch" xlink:to="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Defined Contribution Plan, Employer Matching Contribution, Percent of Match</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of employer matching contribution</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent" xlink:to="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Defined Contribution Plan, Employer Matching Contribution, Percent of Employees' Gross Pay</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Employees compensation percentage</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedContributionPlanCostRecognized" xlink:label="us-gaap_DefinedContributionPlanCostRecognized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanCostRecognized" xlink:to="us-gaap_DefinedContributionPlanCostRecognized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DefinedContributionPlanCostRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Defined Contribution Plan, Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DefinedContributionPlanCostRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contribution cost</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityFairValueDisclosure" xlink:label="us-gaap_EquityFairValueDisclosure" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityFairValueDisclosure" xlink:to="us-gaap_EquityFairValueDisclosure_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity, Fair Value Disclosure</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock fair value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisaggregationOfRevenueTable" xlink:label="us-gaap_DisaggregationOfRevenueTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisaggregationOfRevenueTable" xlink:to="us-gaap_DisaggregationOfRevenueTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisaggregationOfRevenueTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disaggregation of Revenue [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisaggregationOfRevenueLineItems" xlink:label="us-gaap_DisaggregationOfRevenueLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisaggregationOfRevenueLineItems" xlink:to="us-gaap_DisaggregationOfRevenueLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisaggregationOfRevenueLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disaggregation of Revenue [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisaggregationOfRevenueLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REVENUES</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_RevenueIncludingCorporateSegment" xlink:label="cntm_RevenueIncludingCorporateSegment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RevenueIncludingCorporateSegment" xlink:to="cntm_RevenueIncludingCorporateSegment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RevenueIncludingCorporateSegment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of including corporate segments revenue.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RevenueIncludingCorporateSegment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue Including corporate segment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RevenueIncludingCorporateSegment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_RevenueIncludingCorporateSegment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerAssetNet" xlink:label="us-gaap_ContractWithCustomerAssetNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractWithCustomerAssetNet" xlink:to="us-gaap_ContractWithCustomerAssetNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractWithCustomerAssetNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Asset, after Allowance for Credit Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_ContractWithCustomerAssetNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_ContractWithCustomerAssetNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ContractWithCustomerAssetCostsRecognized" xlink:label="cntm_ContractWithCustomerAssetCostsRecognized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ContractWithCustomerAssetCostsRecognized" xlink:to="cntm_ContractWithCustomerAssetCostsRecognized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ContractWithCustomerAssetCostsRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of costs recognized on contracts where performance obligations are completed during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ContractWithCustomerAssetCostsRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Asset, Costs Recognized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ContractWithCustomerAssetCostsRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recognition of costs on contracts where performance obligations completed during the period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ContractWithCustomerAssetDeferralOfCosts" xlink:label="cntm_ContractWithCustomerAssetDeferralOfCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ContractWithCustomerAssetDeferralOfCosts" xlink:to="cntm_ContractWithCustomerAssetDeferralOfCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ContractWithCustomerAssetDeferralOfCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of deferral of costs on contracts where performance obligations were not completed during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ContractWithCustomerAssetDeferralOfCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Asset, Deferral Of Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ContractWithCustomerAssetDeferralOfCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferral of costs on contracts where performance obligations were not complete</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:label="us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:to="us-gaap_ContractWithCustomerLiabilityRevenueRecognized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractWithCustomerLiabilityRevenueRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Liability, Revenue Recognized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_ContractWithCustomerLiabilityRevenueRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recognition of revenue recorded as a contract liability</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ContractWithCustomerLiabilityAdvancePayments" xlink:label="cntm_ContractWithCustomerLiabilityAdvancePayments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ContractWithCustomerLiabilityAdvancePayments" xlink:to="cntm_ContractWithCustomerLiabilityAdvancePayments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ContractWithCustomerLiabilityAdvancePayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of advance payments received from customers for goods or services not yet delivered.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ContractWithCustomerLiabilityAdvancePayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Liability, Advance Payments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ContractWithCustomerLiabilityAdvancePayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer advance payments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ContractWithCustomerLiabilityAdjustmentForCancellationOfContract" xlink:label="cntm_ContractWithCustomerLiabilityAdjustmentForCancellationOfContract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ContractWithCustomerLiabilityAdjustmentForCancellationOfContract" xlink:to="cntm_ContractWithCustomerLiabilityAdjustmentForCancellationOfContract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ContractWithCustomerLiabilityAdjustmentForCancellationOfContract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of decrease in revenue recognized for  adjustment from canceled contract decreases obligation to transfer good or service to customer for which consideration from customer has been received or is due.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ContractWithCustomerLiabilityAdjustmentForCancellationOfContract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Liability, Adjustment for the Cancellation of Contract</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OperatingLossCarryforwardsSubjectToExpiration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Loss Carryforwards, Subject To Expiration</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OperatingLossCarryforwardsIndefinitePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Loss Carryforwards, Indefinite Period</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Type [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CustomerConcentrationRiskMember" xlink:label="us-gaap_CustomerConcentrationRiskMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CustomerConcentrationRiskMember" xlink:to="us-gaap_CustomerConcentrationRiskMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer Concentration Risk [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer concentration risk</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems" xlink:label="us-gaap_SegmentReportingInformationLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingInformationLineItems" xlink:to="us-gaap_SegmentReportingInformationLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment Reporting Information [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REPORTABLE SEGMENTS</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_InterSegmentRevenue" xlink:label="cntm_InterSegmentRevenue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_InterSegmentRevenue" xlink:to="cntm_InterSegmentRevenue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_InterSegmentRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of intersegment revenue.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_InterSegmentRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inter Segment Revenue</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_InterSegmentRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_InterSegmentCostOfRevenue" xlink:label="cntm_InterSegmentCostOfRevenue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_InterSegmentCostOfRevenue" xlink:to="cntm_InterSegmentCostOfRevenue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_InterSegmentCostOfRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of intersegment cost of revenue.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_InterSegmentCostOfRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inter Segment Cost Of Revenue</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_InterSegmentCostOfRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cost of revenue</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfCustomers" xlink:label="cntm_NumberOfCustomers" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfCustomers" xlink:to="cntm_NumberOfCustomers_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfCustomers_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the number of customers.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfCustomers_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Customers</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfCustomers_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of customers</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ManagedSolutionsSegmentMember" xlink:label="cntm_ManagedSolutionsSegmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ManagedSolutionsSegmentMember" xlink:to="cntm_ManagedSolutionsSegmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ManagedSolutionsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the entity's managed solutions segment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ManagedSolutionsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Managed Solutions Segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ManagedSolutionsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Managed Solutions</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LogisticsSegmentMember" xlink:label="cntm_LogisticsSegmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LogisticsSegmentMember" xlink:to="cntm_LogisticsSegmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LogisticsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the entity's logistics segment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LogisticsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Logistics Segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LogisticsSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Logistics</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_TransportationSegmentMember" xlink:label="cntm_TransportationSegmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_TransportationSegmentMember" xlink:to="cntm_TransportationSegmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_TransportationSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the entity's transportation segment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_TransportationSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transportation Segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_TransportationSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transportation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllOtherSegmentsMember" xlink:label="us-gaap_AllOtherSegmentsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllOtherSegmentsMember" xlink:to="us-gaap_AllOtherSegmentsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllOtherSegmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Operating Segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AllOtherSegmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SellingGeneralAndAdministrativeExpenseAbstract" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpenseAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SellingGeneralAndAdministrativeExpenseAbstract" xlink:to="us-gaap_SellingGeneralAndAdministrativeExpenseAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpenseAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, General and Administrative Expense [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpenseAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, general and administrative expenses</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FacilityCost" xlink:label="cntm_FacilityCost" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FacilityCost" xlink:to="cntm_FacilityCost_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FacilityCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of facility expenses.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FacilityCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Facility Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FacilityCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Facility costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeneralInsuranceExpense" xlink:label="us-gaap_GeneralInsuranceExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GeneralInsuranceExpense" xlink:to="us-gaap_GeneralInsuranceExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GeneralInsuranceExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">General Insurance Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GeneralInsuranceExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Insurance expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MarketingExpense" xlink:label="us-gaap_MarketingExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MarketingExpense" xlink:to="us-gaap_MarketingExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MarketingExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Marketing Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MarketingExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Marketing expenses</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_OperationalExpenses" xlink:label="cntm_OperationalExpenses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_OperationalExpenses" xlink:to="cntm_OperationalExpenses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_OperationalExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of operational expenses.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_OperationalExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operational Expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_OperationalExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operational expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LaborAndRelatedExpense" xlink:label="us-gaap_LaborAndRelatedExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LaborAndRelatedExpense" xlink:to="us-gaap_LaborAndRelatedExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LaborAndRelatedExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Labor and Related Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LaborAndRelatedExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Compensation and related benefits</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TravelAndEntertainmentExpense" xlink:label="us-gaap_TravelAndEntertainmentExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TravelAndEntertainmentExpense" xlink:to="us-gaap_TravelAndEntertainmentExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TravelAndEntertainmentExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Travel and Entertainment Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TravelAndEntertainmentExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Travel &amp; entertainment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_VehicleExpenses" xlink:label="cntm_VehicleExpenses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_VehicleExpenses" xlink:to="cntm_VehicleExpenses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_VehicleExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expenses for vehicle.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_VehicleExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vehicle Expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_VehicleExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vehicle expenses</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_Depreciations" xlink:label="cntm_Depreciations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_Depreciations" xlink:to="cntm_Depreciations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_Depreciations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of depreciation expense recognized in the current period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_Depreciations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_Depreciations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentForAmortization" xlink:label="us-gaap_AdjustmentForAmortization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentForAmortization" xlink:to="us-gaap_AdjustmentForAmortization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdjustmentForAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdjustmentForAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_WorkingCapitalAdjustment" xlink:label="cntm_WorkingCapitalAdjustment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_WorkingCapitalAdjustment" xlink:to="cntm_WorkingCapitalAdjustment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_WorkingCapitalAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase decrease in working capital in case of mergers and acquisition.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_WorkingCapitalAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Working Capital Adjustment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_WorkingCapitalAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">MSA Working Capital Adjustment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetImpairment" xlink:label="us-gaap_GoodwillAndIntangibleAssetImpairment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetImpairment" xlink:to="us-gaap_GoodwillAndIntangibleAssetImpairment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillAndIntangibleAssetImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill and Intangible Asset Impairment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GoodwillAndIntangibleAssetImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on impairment of intangible assets and goodwill</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_GoodwillAndIntangibleAssetImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on impairment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:label="us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:to="us-gaap_SegmentExpenditureAdditionToLongLivedAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentExpenditureAdditionToLongLivedAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment, Expenditure, Addition to Long-Lived Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentExpenditureAdditionToLongLivedAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital expenditures</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReportableSegmentAggregationBeforeOtherOperatingSegmentMember" xlink:label="us-gaap_ReportableSegmentAggregationBeforeOtherOperatingSegmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ReportableSegmentAggregationBeforeOtherOperatingSegmentMember" xlink:to="us-gaap_ReportableSegmentAggregationBeforeOtherOperatingSegmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ReportableSegmentAggregationBeforeOtherOperatingSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reportable Segment, Aggregation before Other Operating Segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ReportableSegmentAggregationBeforeOtherOperatingSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reportable Segment, Aggregation before Other Operating Segment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTable" xlink:label="us-gaap_SubsequentEventTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTable" xlink:to="us-gaap_SubsequentEventTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupDisposedOfByMeansOtherThanSaleNotDiscontinuedOperationsExchangeMember" xlink:label="us-gaap_DisposalGroupDisposedOfByMeansOtherThanSaleNotDiscontinuedOperationsExchangeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisposalGroupDisposedOfByMeansOtherThanSaleNotDiscontinuedOperationsExchangeMember" xlink:to="us-gaap_DisposalGroupDisposedOfByMeansOtherThanSaleNotDiscontinuedOperationsExchangeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisposalGroupDisposedOfByMeansOtherThanSaleNotDiscontinuedOperationsExchangeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Disposed of by Means Other than Sale, Not Discontinued Operations, Exchange [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisposalGroupDisposedOfByMeansOtherThanSaleNotDiscontinuedOperationsExchangeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal by means other than sale</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GlobalImpexIncMember" xlink:label="cntm_GlobalImpexIncMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GlobalImpexIncMember" xlink:to="cntm_GlobalImpexIncMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GlobalImpexIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Global Impex Inc.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GlobalImpexIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Global Impex Inc [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GlobalImpexIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">GIX</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AstrabridgeIncMember" xlink:label="cntm_AstrabridgeIncMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AstrabridgeIncMember" xlink:to="cntm_AstrabridgeIncMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AstrabridgeIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to AstraBridge Inc.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AstrabridgeIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AstraBridge Inc [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AstrabridgeIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AstraBridge Inc.</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BlueCloudSoftechSolutionsLimitedMember" xlink:label="cntm_BlueCloudSoftechSolutionsLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BlueCloudSoftechSolutionsLimitedMember" xlink:to="cntm_BlueCloudSoftechSolutionsLimitedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BlueCloudSoftechSolutionsLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Blue Cloud Softech Solutions Limited.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BlueCloudSoftechSolutionsLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Blue Cloud Softech Solutions Limited [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BlueCloudSoftechSolutionsLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Blue Cloud</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:to="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Benchmark [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskBenchmarkDomain" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Benchmark [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SalesRevenueNetMember" xlink:label="us-gaap_SalesRevenueNetMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SalesRevenueNetMember" xlink:to="us-gaap_SalesRevenueNetMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SalesRevenueNetMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue Benchmark [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SalesRevenueNetMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sales revenue net member</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeographicConcentrationRiskMember" xlink:label="us-gaap_GeographicConcentrationRiskMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GeographicConcentrationRiskMember" xlink:to="us-gaap_GeographicConcentrationRiskMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GeographicConcentrationRiskMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Geographic Concentration Risk [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GeographicConcentrationRiskMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Geography</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventLineItems" xlink:label="us-gaap_SubsequentEventLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="us-gaap_SubsequentEventLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SUBSEQUENT EVENTS</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PercentageOfEquityInterestDisposed" xlink:label="cntm_PercentageOfEquityInterestDisposed" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PercentageOfEquityInterestDisposed" xlink:to="cntm_PercentageOfEquityInterestDisposed_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PercentageOfEquityInterestDisposed_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of equity interest disposed.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PercentageOfEquityInterestDisposed_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage Of Equity Interest Disposed</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PercentageOfEquityInterestDisposed_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of interest disposed</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharesReceivedOrReceivable" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharesReceivedOrReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharesReceivedOrReceivable" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharesReceivedOrReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharesReceivedOrReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate number of shares received or receivable as consideration in connection with the disposal by means other than sale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharesReceivedOrReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Consideration, Equity Shares Received Or Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharesReceivedOrReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity consideration</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesFaceValuePerShare" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesFaceValuePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesFaceValuePerShare" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesFaceValuePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesFaceValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Face value per share of equity instrument received or receivable in connection with the disposal.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesFaceValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Equity Shares, Face Value Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesFaceValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity consideration, face value per share</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharePricePerShare" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharePricePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharePricePerShare" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharePricePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharePricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Per share price at which the equity shares are received or receivable as consideration in a share swap transaction upon disposal by means other than sale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharePricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Consideration, Equity Share, Price Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationConsiderationEquitySharePricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity consideration, price per share</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationNumberOfSharesExchanged" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNumberOfSharesExchanged" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationNumberOfSharesExchanged" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationNumberOfSharesExchanged_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNumberOfSharesExchanged_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares exchanged in share swap as part of disposal by means other than sale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNumberOfSharesExchanged_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Number Of Shares Exchanged</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationNumberOfSharesExchanged_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares exchanged</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationShareSwapRatio" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationShareSwapRatio" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationShareSwapRatio" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationShareSwapRatio_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationShareSwapRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The exchange ratio established in a share swap transaction for a disposal group, including a discontinued operation, representing the number of equity shares issued by the acquirer in exchange for the equity interests of the disposed entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationShareSwapRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Share Swap Ratio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationShareSwapRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Swap ratio</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesReceivedOrReceivable" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesReceivedOrReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesReceivedOrReceivable" xlink:to="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesReceivedOrReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesReceivedOrReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares received or receivable upon exchange in a share swap transaction by the shareholders of the disposed entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesReceivedOrReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disposal Group, Including Discontinued Operation, Equity Shares Received Or Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DisposalGroupIncludingDiscontinuedOperationEquitySharesReceivedOrReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares received upon exchange</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PostShareSwapTransactionEquityOwnershipPercentageHeldByEntity" xlink:label="cntm_PostShareSwapTransactionEquityOwnershipPercentageHeldByEntity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PostShareSwapTransactionEquityOwnershipPercentageHeldByEntity" xlink:to="cntm_PostShareSwapTransactionEquityOwnershipPercentageHeldByEntity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PostShareSwapTransactionEquityOwnershipPercentageHeldByEntity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of equity ownership to be held by the entity post share swap transaction.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PostShareSwapTransactionEquityOwnershipPercentageHeldByEntity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Post Share Swap Transaction, Equity Ownership Percentage Held By Entity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PostShareSwapTransactionEquityOwnershipPercentageHeldByEntity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of ownership held by entity post swap transaction</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PostShareSwapTransactionSharesTransferLockInPeriod" xlink:label="cntm_PostShareSwapTransactionSharesTransferLockInPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PostShareSwapTransactionSharesTransferLockInPeriod" xlink:to="cntm_PostShareSwapTransactionSharesTransferLockInPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PostShareSwapTransactionSharesTransferLockInPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period during which the consideration shares received in the share swap transaction are subject to regulatory restrictions on transfer or sale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PostShareSwapTransactionSharesTransferLockInPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Post Share Swap Transaction, Shares Transfer, Lock In Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PostShareSwapTransactionSharesTransferLockInPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share transfer lock in period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskPercentage1" xlink:label="us-gaap_ConcentrationRiskPercentage1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskPercentage1" xlink:to="us-gaap_ConcentrationRiskPercentage1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration risk percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_HarryKahnAssociatesIncMember" xlink:label="cntm_HarryKahnAssociatesIncMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_HarryKahnAssociatesIncMember" xlink:to="cntm_HarryKahnAssociatesIncMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_HarryKahnAssociatesIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Harry Kahn Associates, Inc.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_HarryKahnAssociatesIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Harry Kahn Associates, Inc [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_HarryKahnAssociatesIncMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Harry Kahn Associates, Inc</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:to="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Percentage of Voting Interests Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of voting interest acquired</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:label="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:to="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Equity Interest Issued or Issuable, Number of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination, number of shares issued</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationPromissoryNoteReceivable" xlink:label="cntm_BusinessCombinationPromissoryNoteReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationPromissoryNoteReceivable" xlink:to="cntm_BusinessCombinationPromissoryNoteReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationPromissoryNoteReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of promissory note receivable from acquiree in connection with the acquisition transaction.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationPromissoryNoteReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Promissory Note Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationPromissoryNoteReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Promissory note receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireBusinessesGross" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireBusinessesGross" xlink:to="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Businesses, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to acquire business</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAssumed1" xlink:label="us-gaap_LiabilitiesAssumed1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAssumed1" xlink:to="us-gaap_LiabilitiesAssumed1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesAssumed1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities Assumed</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesAssumed1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Third party debt assumed</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PeriodOfTerminationSettlementWithPrimeContractor" xlink:label="cntm_PeriodOfTerminationSettlementWithPrimeContractor" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PeriodOfTerminationSettlementWithPrimeContractor" xlink:to="cntm_PeriodOfTerminationSettlementWithPrimeContractor_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PeriodOfTerminationSettlementWithPrimeContractor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period over which the termination settlement will be paid to the prime contractor.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PeriodOfTerminationSettlementWithPrimeContractor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period Of Termination Settlement With Prime Contractor</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PeriodOfTerminationSettlementWithPrimeContractor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period of settlement with prime contractor</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_TerminatedContractAmountOwnedToSubcontractorPriorToTermination" xlink:label="cntm_TerminatedContractAmountOwnedToSubcontractorPriorToTermination" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_TerminatedContractAmountOwnedToSubcontractorPriorToTermination" xlink:to="cntm_TerminatedContractAmountOwnedToSubcontractorPriorToTermination_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_TerminatedContractAmountOwnedToSubcontractorPriorToTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount owed to subcontractor for the services received prior to termination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_TerminatedContractAmountOwnedToSubcontractorPriorToTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Terminated Contract, Amount Owned To Subcontractor Prior To Termination</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_TerminatedContractAmountOwnedToSubcontractorPriorToTermination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount owed to subcontractor</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_TerminatedContractProportionateShareOfTerminationProceedsOfferedToSubcontractor" xlink:label="cntm_TerminatedContractProportionateShareOfTerminationProceedsOfferedToSubcontractor" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_TerminatedContractProportionateShareOfTerminationProceedsOfferedToSubcontractor" xlink:to="cntm_TerminatedContractProportionateShareOfTerminationProceedsOfferedToSubcontractor_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_TerminatedContractProportionateShareOfTerminationProceedsOfferedToSubcontractor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of proportionate share of termination proceeds owed to subcontractor.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_TerminatedContractProportionateShareOfTerminationProceedsOfferedToSubcontractor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Terminated Contract, Proportionate Share Of Termination Proceeds Offered To Subcontractor</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_TerminatedContractProportionateShareOfTerminationProceedsOfferedToSubcontractor_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proportionate share of termination proceeds offered</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BridgeNoteMember" xlink:label="cntm_BridgeNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BridgeNoteMember" xlink:to="cntm_BridgeNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to bridge note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bridge Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bridge note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FirstBridgeNoteMember" xlink:label="cntm_FirstBridgeNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FirstBridgeNoteMember" xlink:to="cntm_FirstBridgeNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FirstBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to first bridge note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FirstBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">First Bridge Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FirstBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">First Bridge Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SecondBridgeNoteMember" xlink:label="cntm_SecondBridgeNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SecondBridgeNoteMember" xlink:to="cntm_SecondBridgeNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SecondBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to second bridge note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SecondBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second Bridge Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SecondBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second Bridge Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ThirdBridgeNoteMember" xlink:label="cntm_ThirdBridgeNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ThirdBridgeNoteMember" xlink:to="cntm_ThirdBridgeNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ThirdBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to third bridge note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ThirdBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Third Bridge Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ThirdBridgeNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Third Bridge Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertiblePromissoryNoteMember" xlink:label="cntm_ConvertiblePromissoryNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertiblePromissoryNoteMember" xlink:to="cntm_ConvertiblePromissoryNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertiblePromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to a convertible promissory note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertiblePromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Promissory Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertiblePromissoryNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible promissory note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FirstConvertibleNoteMember" xlink:label="cntm_FirstConvertibleNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FirstConvertibleNoteMember" xlink:to="cntm_FirstConvertibleNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FirstConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to First Convertible Note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FirstConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">First Convertible Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FirstConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">First Convertible Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SecondConvertibleNoteMember" xlink:label="cntm_SecondConvertibleNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SecondConvertibleNoteMember" xlink:to="cntm_SecondConvertibleNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SecondConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Second Convertible Note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SecondConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second Convertible Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SecondConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second Convertible Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ThirdConvertibleNoteMember" xlink:label="cntm_ThirdConvertibleNoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ThirdConvertibleNoteMember" xlink:to="cntm_ThirdConvertibleNoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ThirdConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Third Convertible Note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ThirdConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Third Convertible Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ThirdConvertibleNoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Third Convertible Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNoteIssuedOnDecember82025Member" xlink:label="cntm_ConvertibleNoteIssuedOnDecember82025Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNoteIssuedOnDecember82025Member" xlink:to="cntm_ConvertibleNoteIssuedOnDecember82025Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNoteIssuedOnDecember82025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to convertible note issued on December 8, 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNoteIssuedOnDecember82025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Note Issued On December 8, 2025 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNoteIssuedOnDecember82025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible note issued on December 8, 2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfPromissoryNote" xlink:label="cntm_NumberOfPromissoryNote" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfPromissoryNote" xlink:to="cntm_NumberOfPromissoryNote_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfPromissoryNote_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of promissory note issued during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfPromissoryNote_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Promissory Note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentFacilitationFeeAmount" xlink:label="cntm_DebtInstrumentFacilitationFeeAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentFacilitationFeeAmount" xlink:to="cntm_DebtInstrumentFacilitationFeeAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentFacilitationFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of facilitation fee payable to lender.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentFacilitationFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Facilitation Fee, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentFacilitationFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Facilitation fee, amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentFacilitationFeePercentage" xlink:label="cntm_DebtInstrumentFacilitationFeePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentFacilitationFeePercentage" xlink:to="cntm_DebtInstrumentFacilitationFeePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentFacilitationFeePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of facilitation fee payable to lender.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentFacilitationFeePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Facilitation Fee, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentFacilitationFeePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Facilitation fee, percent</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentDebtDefaultInterestRatePercentage" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRatePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentDebtDefaultInterestRatePercentage" xlink:to="cntm_DebtInstrumentDebtDefaultInterestRatePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of interest rate on the debt instrument in the event of default.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Debt Default, Interest Rate, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest rate on default</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentDebtDefaultLatePaymentFeePercentage" xlink:label="cntm_DebtInstrumentDebtDefaultLatePaymentFeePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentDebtDefaultLatePaymentFeePercentage" xlink:to="cntm_DebtInstrumentDebtDefaultLatePaymentFeePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentDebtDefaultLatePaymentFeePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of late payment fee charged on the outstanding amount upon occurrence of default.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentDebtDefaultLatePaymentFeePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Debt Default, Late Payment Fee, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentDebtDefaultLatePaymentFeePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Late payment fee, percent</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebInstrumentNumberOfConvertibleDebtFinancing" xlink:label="cntm_DebInstrumentNumberOfConvertibleDebtFinancing" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebInstrumentNumberOfConvertibleDebtFinancing" xlink:to="cntm_DebInstrumentNumberOfConvertibleDebtFinancing_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebInstrumentNumberOfConvertibleDebtFinancing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of convertible debt financing entered.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebInstrumentNumberOfConvertibleDebtFinancing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deb Instrument, Number Of Convertible Debt Financing</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebInstrumentNumberOfConvertibleDebtFinancing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of convertible debt financing</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentNumberOfUnaffiliatedAccreditedInvestors" xlink:label="cntm_DebtInstrumentNumberOfUnaffiliatedAccreditedInvestors" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentNumberOfUnaffiliatedAccreditedInvestors" xlink:to="cntm_DebtInstrumentNumberOfUnaffiliatedAccreditedInvestors_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentNumberOfUnaffiliatedAccreditedInvestors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of unaffiliated accredited investor to whom the debt instrument was issued.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentNumberOfUnaffiliatedAccreditedInvestors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Number Of Unaffiliated Accredited Investors</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentNumberOfUnaffiliatedAccreditedInvestors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Separate convertible note unaffiliated</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GrossProceedsFromConvertibleDebt" xlink:label="cntm_GrossProceedsFromConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GrossProceedsFromConvertibleDebt" xlink:to="cntm_GrossProceedsFromConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GrossProceedsFromConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gross proceeds from convertible debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GrossProceedsFromConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross Proceeds From Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GrossProceedsFromConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross proceeds from convertible debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentNumberOfCommitmentSharesIssued" xlink:label="cntm_DebtInstrumentNumberOfCommitmentSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentNumberOfCommitmentSharesIssued" xlink:to="cntm_DebtInstrumentNumberOfCommitmentSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentNumberOfCommitmentSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of commitment shares issued in connection with the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentNumberOfCommitmentSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Number Of Commitment Shares Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentNumberOfCommitmentSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of commitment shares issued</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentPurchasePriceNetOfIssueDiscount" xlink:label="cntm_DebtInstrumentPurchasePriceNetOfIssueDiscount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentPurchasePriceNetOfIssueDiscount" xlink:to="cntm_DebtInstrumentPurchasePriceNetOfIssueDiscount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentPurchasePriceNetOfIssueDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of purchase price of debt instrument, net of issue discount.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentPurchasePriceNetOfIssueDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument, Purchase Price, Net Of Issue Discount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentPurchasePriceNetOfIssueDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase price</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentOriginalIssueDiscount" xlink:label="cntm_DebtInstrumentOriginalIssueDiscount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentOriginalIssueDiscount" xlink:to="cntm_DebtInstrumentOriginalIssueDiscount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentOriginalIssueDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of non-cash expense for the original issuance discount incurred on the debt instruments during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentOriginalIssueDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Original Issue Discount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentOriginalIssueDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of non-cash expense for the original issuance discount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PaymentsForLegalFeeReimbursement" xlink:label="cntm_PaymentsForLegalFeeReimbursement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentsForLegalFeeReimbursement" xlink:to="cntm_PaymentsForLegalFeeReimbursement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentsForLegalFeeReimbursement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash outflow as legal fees reimbursement in connection with the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentsForLegalFeeReimbursement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments For Legal Fee Reimbursement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PaymentsForLegalFeeReimbursement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments for legal fees reimbursement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PaymentsForDueDiligenceFees" xlink:label="cntm_PaymentsForDueDiligenceFees" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentsForDueDiligenceFees" xlink:to="cntm_PaymentsForDueDiligenceFees_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentsForDueDiligenceFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash outflow as due diligence fees in connection with the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentsForDueDiligenceFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments For Due Diligence Fees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PaymentsForDueDiligenceFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments for due diligence fees</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentRepaymentObligationAmount" xlink:label="cntm_DebtInstrumentRepaymentObligationAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRepaymentObligationAmount" xlink:to="cntm_DebtInstrumentRepaymentObligationAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRepaymentObligationAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of repayment obligation of debt instrument, including interest.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRepaymentObligationAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Repayment Obligation, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRepaymentObligationAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate repayment obligation</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentRepaymentNumberOfInstallmentsForPeriodicPayments" xlink:label="cntm_DebtInstrumentRepaymentNumberOfInstallmentsForPeriodicPayments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRepaymentNumberOfInstallmentsForPeriodicPayments" xlink:to="cntm_DebtInstrumentRepaymentNumberOfInstallmentsForPeriodicPayments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRepaymentNumberOfInstallmentsForPeriodicPayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of installments for periodic payment of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRepaymentNumberOfInstallmentsForPeriodicPayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Repayment, Number Of Installments For Periodic Payments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRepaymentNumberOfInstallmentsForPeriodicPayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of installments for periodic payments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentRepaymentPaymentDeferralPeriod" xlink:label="cntm_DebtInstrumentRepaymentPaymentDeferralPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRepaymentPaymentDeferralPeriod" xlink:to="cntm_DebtInstrumentRepaymentPaymentDeferralPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRepaymentPaymentDeferralPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period during which the payments are temporarily postponed before scheduled repayment begins under the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRepaymentPaymentDeferralPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Repayment, Payment Deferral Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRepaymentPaymentDeferralPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument, repayment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentIntervalFrequencyOfPeriodicPayment" xlink:label="cntm_DebtInstrumentIntervalFrequencyOfPeriodicPayment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentIntervalFrequencyOfPeriodicPayment" xlink:to="cntm_DebtInstrumentIntervalFrequencyOfPeriodicPayment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentIntervalFrequencyOfPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interval frequency of periodic payments of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentIntervalFrequencyOfPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Interval Frequency of Periodic Payment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentIntervalFrequencyOfPeriodicPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument, interval</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PercentageOfConvertibleBeneficialOwnershipLimitation" xlink:label="cntm_PercentageOfConvertibleBeneficialOwnershipLimitation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PercentageOfConvertibleBeneficialOwnershipLimitation" xlink:to="cntm_PercentageOfConvertibleBeneficialOwnershipLimitation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PercentageOfConvertibleBeneficialOwnershipLimitation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of conversion notice, subject to beneficial ownership limitation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PercentageOfConvertibleBeneficialOwnershipLimitation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage Of Convertible Beneficial Ownership Limitation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PercentageOfConvertibleBeneficialOwnershipLimitation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beneficial ownership limitation</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentDebtDefaultOutstandingBalanceIncludingAccruedInterestAndFeesPercentage" xlink:label="cntm_DebtInstrumentDebtDefaultOutstandingBalanceIncludingAccruedInterestAndFeesPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentDebtDefaultOutstandingBalanceIncludingAccruedInterestAndFeesPercentage" xlink:to="cntm_DebtInstrumentDebtDefaultOutstandingBalanceIncludingAccruedInterestAndFeesPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentDebtDefaultOutstandingBalanceIncludingAccruedInterestAndFeesPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of outstanding debt payable upon occurrence of default under the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentDebtDefaultOutstandingBalanceIncludingAccruedInterestAndFeesPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Debt Default, Outstanding Balance Including Accrued Interest And Fees, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentDebtDefaultOutstandingBalanceIncludingAccruedInterestAndFeesPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding debt percentage in default</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentConvertibleConversionPriceDeterminationThresholdTradingDays" xlink:label="cntm_DebtInstrumentConvertibleConversionPriceDeterminationThresholdTradingDays" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConvertibleConversionPriceDeterminationThresholdTradingDays" xlink:to="cntm_DebtInstrumentConvertibleConversionPriceDeterminationThresholdTradingDays_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConvertibleConversionPriceDeterminationThresholdTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold number of specified trading days considered in determination of lowest volume weighted average price for conversion price.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConvertibleConversionPriceDeterminationThresholdTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Conversion Price Determination, Threshold Trading Days</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConvertibleConversionPriceDeterminationThresholdTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion, threshold trading days</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PaymentsForPlacementAgentFees" xlink:label="cntm_PaymentsForPlacementAgentFees" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentsForPlacementAgentFees" xlink:to="cntm_PaymentsForPlacementAgentFees_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentsForPlacementAgentFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash outflow for placement agent fees in connection with the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentsForPlacementAgentFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments For Placement Agent Fees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PaymentsForPlacementAgentFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments for placement agent fees</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentOneTimeInterestChargeAmount" xlink:label="cntm_DebtInstrumentOneTimeInterestChargeAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentOneTimeInterestChargeAmount" xlink:to="cntm_DebtInstrumentOneTimeInterestChargeAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentOneTimeInterestChargeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of one-time interest charge on the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentOneTimeInterestChargeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, One Time Interest Charge, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentOneTimeInterestChargeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">One time interest amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentRepaymentNumberOfInstallments" xlink:label="cntm_DebtInstrumentRepaymentNumberOfInstallments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRepaymentNumberOfInstallments" xlink:to="cntm_DebtInstrumentRepaymentNumberOfInstallments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRepaymentNumberOfInstallments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of installments for repayment of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRepaymentNumberOfInstallments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Repayment, Number Of Installments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRepaymentNumberOfInstallments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of installments for repayment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentRepaymentFinalInstallmentAmount" xlink:label="cntm_DebtInstrumentRepaymentFinalInstallmentAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRepaymentFinalInstallmentAmount" xlink:to="cntm_DebtInstrumentRepaymentFinalInstallmentAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRepaymentFinalInstallmentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Final installment for repayment of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRepaymentFinalInstallmentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Repayment, Final Installment, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRepaymentFinalInstallmentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Final installment, amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentRepaymentEachInstallmentGracePeriod" xlink:label="cntm_DebtInstrumentRepaymentEachInstallmentGracePeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRepaymentEachInstallmentGracePeriod" xlink:to="cntm_DebtInstrumentRepaymentEachInstallmentGracePeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRepaymentEachInstallmentGracePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period of time allowed for each installment to repay debt without incurring penalty or default.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRepaymentEachInstallmentGracePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Repayment, Each Installment, Grace Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRepaymentEachInstallmentGracePeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Grace period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentDebtDefaultConvertibleConversionPricePercentageOfLowestTradingPrice" xlink:label="cntm_DebtInstrumentDebtDefaultConvertibleConversionPricePercentageOfLowestTradingPrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentDebtDefaultConvertibleConversionPricePercentageOfLowestTradingPrice" xlink:to="cntm_DebtInstrumentDebtDefaultConvertibleConversionPricePercentageOfLowestTradingPrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentDebtDefaultConvertibleConversionPricePercentageOfLowestTradingPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion price as percentage of lowest trading price of convertible debt instrument in the event of default.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentDebtDefaultConvertibleConversionPricePercentageOfLowestTradingPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Debt Default, Convertible, Conversion Price, Percentage Of Lowest Trading Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentDebtDefaultConvertibleConversionPricePercentageOfLowestTradingPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt default conversion price, percentage of lowest trading price</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentDebtDefaultConvertibleConversionPriceThresholdTradingDays" xlink:label="cntm_DebtInstrumentDebtDefaultConvertibleConversionPriceThresholdTradingDays" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentDebtDefaultConvertibleConversionPriceThresholdTradingDays" xlink:to="cntm_DebtInstrumentDebtDefaultConvertibleConversionPriceThresholdTradingDays_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentDebtDefaultConvertibleConversionPriceThresholdTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold number of specified trading days considered in determination of lowest trading price for conversion price.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentDebtDefaultConvertibleConversionPriceThresholdTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Debt Default, Convertible, Conversion Price, Threshold Trading Days</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentDebtDefaultConvertibleConversionPriceThresholdTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt default conversion price, threshold trading days</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentConversionBeneficialOwnershipLimitationPercentage" xlink:label="cntm_DebtInstrumentConversionBeneficialOwnershipLimitationPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConversionBeneficialOwnershipLimitationPercentage" xlink:to="cntm_DebtInstrumentConversionBeneficialOwnershipLimitationPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConversionBeneficialOwnershipLimitationPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of beneficial ownership limitation of the convertible debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConversionBeneficialOwnershipLimitationPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Conversion, Beneficial Ownership Limitation, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConversionBeneficialOwnershipLimitationPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beneficial ownership limitation, percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentDebtDefaultInContinuationOutstandingBalanceIncludingAccruedInterestAndFeesPercentage" xlink:label="cntm_DebtInstrumentDebtDefaultInContinuationOutstandingBalanceIncludingAccruedInterestAndFeesPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentDebtDefaultInContinuationOutstandingBalanceIncludingAccruedInterestAndFeesPercentage" xlink:to="cntm_DebtInstrumentDebtDefaultInContinuationOutstandingBalanceIncludingAccruedInterestAndFeesPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentDebtDefaultInContinuationOutstandingBalanceIncludingAccruedInterestAndFeesPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of outstanding debt payable upon occurrence and continuation of default under the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentDebtDefaultInContinuationOutstandingBalanceIncludingAccruedInterestAndFeesPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Debt Default In Continuation, Outstanding Balance Including Accrued Interest And Fees, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentDebtDefaultInContinuationOutstandingBalanceIncludingAccruedInterestAndFeesPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Continuing default, outstanding balance payable, percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentConvertibleConversionPriceDeterminationPercentageOfLowestDailyVolumeWeightedAveragePrice" xlink:label="cntm_DebtInstrumentConvertibleConversionPriceDeterminationPercentageOfLowestDailyVolumeWeightedAveragePrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConvertibleConversionPriceDeterminationPercentageOfLowestDailyVolumeWeightedAveragePrice" xlink:to="cntm_DebtInstrumentConvertibleConversionPriceDeterminationPercentageOfLowestDailyVolumeWeightedAveragePrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConvertibleConversionPriceDeterminationPercentageOfLowestDailyVolumeWeightedAveragePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of lowest daily volume weighted average price of common stock considered in determination of conversion price of convertible debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConvertibleConversionPriceDeterminationPercentageOfLowestDailyVolumeWeightedAveragePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Conversion Price Determination, Percentage Of Lowest Daily Volume Weighted Average Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConvertibleConversionPriceDeterminationPercentageOfLowestDailyVolumeWeightedAveragePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion price determination, percentage of lowest VWAP</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentUnpaidPrincipalUponMaturityInterestRatePercentage" xlink:label="cntm_DebtInstrumentUnpaidPrincipalUponMaturityInterestRatePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentUnpaidPrincipalUponMaturityInterestRatePercentage" xlink:to="cntm_DebtInstrumentUnpaidPrincipalUponMaturityInterestRatePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentUnpaidPrincipalUponMaturityInterestRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of interest charged for unpaid principal amount upon maturity for a debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentUnpaidPrincipalUponMaturityInterestRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Unpaid Principal Upon Maturity, Interest Rate, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentUnpaidPrincipalUponMaturityInterestRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unpaid principal on maturity, interest rate</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentConvertibleConversionPricePercentageOfLowestTradingPrice" xlink:label="cntm_DebtInstrumentConvertibleConversionPricePercentageOfLowestTradingPrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConvertibleConversionPricePercentageOfLowestTradingPrice" xlink:to="cntm_DebtInstrumentConvertibleConversionPricePercentageOfLowestTradingPrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConvertibleConversionPricePercentageOfLowestTradingPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion price as percentage of lowest trading price of convertible debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConvertibleConversionPricePercentageOfLowestTradingPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Conversion Price, Percentage Of Lowest Trading Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConvertibleConversionPricePercentageOfLowestTradingPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion price, percentage of lowest trading price</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtConversionOriginalDebtAmount1" xlink:label="us-gaap_DebtConversionOriginalDebtAmount1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtConversionOriginalDebtAmount1" xlink:to="us-gaap_DebtConversionOriginalDebtAmount1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtConversionOriginalDebtAmount1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Conversion, Original Debt, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtConversionOriginalDebtAmount1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible debt amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtDefaultLongtermDebtAmount" xlink:label="us-gaap_DebtDefaultLongtermDebtAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtDefaultLongtermDebtAmount" xlink:to="us-gaap_DebtDefaultLongtermDebtAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtDefaultLongtermDebtAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Debt Default, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtDefaultLongtermDebtAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt default, amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GainLossOnExtinguishmentOfContingentConsiderationLiability" xlink:label="cntm_GainLossOnExtinguishmentOfContingentConsiderationLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GainLossOnExtinguishmentOfContingentConsiderationLiability" xlink:to="cntm_GainLossOnExtinguishmentOfContingentConsiderationLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GainLossOnExtinguishmentOfContingentConsiderationLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain or loss recognized during the period resulting from the extinguishment, settlement, termination, or cancellation of earnout obligations under a contingent earnout arrangement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GainLossOnExtinguishmentOfContingentConsiderationLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Extinguishment of Contingent Consideration Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GainLossOnExtinguishmentOfContingentConsiderationLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on extinguishment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1" xlink:label="us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1" xlink:to="us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncash or Part Noncash Acquisition, Debt Assumed</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisitions</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NoncashOrPartNoncashAcquisitionDebtAssumed1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying value of debt exchanged in connection with acquisition of non-controlling shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ReverseRecapitalizationAbstract" xlink:label="cntm_ReverseRecapitalizationAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ReverseRecapitalizationAbstract" xlink:to="cntm_ReverseRecapitalizationAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ReverseRecapitalizationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">No definition available.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ReverseRecapitalizationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REVERSE RECAPITALIZATION</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ReverseRecapitalizationTextBlock" xlink:label="cntm_ReverseRecapitalizationTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ReverseRecapitalizationTextBlock" xlink:to="cntm_ReverseRecapitalizationTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ReverseRecapitalizationTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The entire disclosure for reverse recapitalization.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ReverseRecapitalizationTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reverse Recapitalization [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ReverseRecapitalizationTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REVERSE RECAPITALIZATION</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:label="us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:to="us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ACQUISITIONS</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AcquisitionsTextBlock" xlink:label="cntm_AcquisitionsTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AcquisitionsTextBlock" xlink:to="cntm_AcquisitionsTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AcquisitionsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The entire disclosure for business combination and asset acquisition.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AcquisitionsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisitions [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AcquisitionsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ACQUISITIONS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:to="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill and Intangible Assets Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">GOODWILL AND INTANGIBLE ASSETS, NET</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentAbstract" xlink:label="us-gaap_PropertyPlantAndEquipmentAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentAbstract" xlink:to="us-gaap_PropertyPlantAndEquipmentAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">PROPERTY AND EQUIPMENT, NET</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:label="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:to="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">PROPERTY AND EQUIPMENT, NET</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:to="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">STOCK-BASED COMPENSATION</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:to="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">STOCK-BASED COMPENSATION</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:to="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DERIVATIVE FINANCIAL INSTRUMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:to="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Instruments and Hedging Activities Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DERIVATIVE FINANCIAL INSTRUMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeDisclosureAbstract" xlink:label="us-gaap_LesseeDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeDisclosureAbstract" xlink:to="us-gaap_LesseeDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">LEASES</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LeaseDisclosureTextBlock" xlink:label="cntm_LeaseDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LeaseDisclosureTextBlock" xlink:to="cntm_LeaseDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LeaseDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The entire disclosure of information about leases.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LeaseDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lease Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LeaseDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">LEASES</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EmployeeRetentionCreditDisclosureAbstract" xlink:label="cntm_EmployeeRetentionCreditDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EmployeeRetentionCreditDisclosureAbstract" xlink:to="cntm_EmployeeRetentionCreditDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EmployeeRetentionCreditDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">n/a</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EmployeeRetentionCreditDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">EMPLOYEE RETENTION CREDIT (ERC)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EmployeeRetentionCreditDisclosureTextBlock" xlink:label="cntm_EmployeeRetentionCreditDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EmployeeRetentionCreditDisclosureTextBlock" xlink:to="cntm_EmployeeRetentionCreditDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EmployeeRetentionCreditDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The entire disclosure pertaining to the employee retention credit.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EmployeeRetentionCreditDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Employee Retention Credit Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EmployeeRetentionCreditDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">EMPLOYEE RETENTION CREDIT (ERC)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ReverseStockSplitAbstract" xlink:label="cntm_ReverseStockSplitAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ReverseStockSplitAbstract" xlink:to="cntm_ReverseStockSplitAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ReverseStockSplitAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">No definition available.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ReverseStockSplitAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REVERSE STOCK SPLIT</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ReverseStockSplitTextBlock" xlink:label="cntm_ReverseStockSplitTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ReverseStockSplitTextBlock" xlink:to="cntm_ReverseStockSplitTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ReverseStockSplitTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The entire disclosure about reverse stock split.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ReverseStockSplitTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reverse Stock Split [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ReverseStockSplitTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REVERSE STOCK SPLIT</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ScheduleOfReverseRecapitalizationTableTextBlock" xlink:label="cntm_ScheduleOfReverseRecapitalizationTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ScheduleOfReverseRecapitalizationTableTextBlock" xlink:to="cntm_ScheduleOfReverseRecapitalizationTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ScheduleOfReverseRecapitalizationTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular disclosure of reverse recapitalization relating reconciliation of business combination to the consolidated statements of cash flows and the consolidated statements of changes in stockholders' deficit and number of shares issued following the consummation of the business combination</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ScheduleOfReverseRecapitalizationTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule Of Reverse Recapitalization [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ScheduleOfReverseRecapitalizationTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of reverse recapitalization</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Business Acquisitions, by Acquisition [Table]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DeliverycircleLlcMember" xlink:label="cntm_DeliverycircleLlcMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DeliverycircleLlcMember" xlink:to="cntm_DeliverycircleLlcMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DeliverycircleLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to DeliveryCircle LLC.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DeliverycircleLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DeliveryCircle LLC [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DeliverycircleLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Delivery Circle LLC</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionLineItems" xlink:label="us-gaap_BusinessAcquisitionLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionLineItems" xlink:to="us-gaap_BusinessAcquisitionLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ACQUISITIONS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionTableTextBlock" xlink:label="us-gaap_AssetAcquisitionTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionTableTextBlock" xlink:to="us-gaap_AssetAcquisitionTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetAcquisitionTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of asset acquisition</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:to="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Business Acquisitions, by Acquisition [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of fair value of the purchase consideration in the acquisition</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:label="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:to="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Recognized Identified Assets Acquired and Liabilities Assumed [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of fair values of the assets acquired and liabilities assumed in the acquisition</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedAndIndefiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTableTextBlock" xlink:label="us-gaap_FiniteLivedAndIndefiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedAndIndefiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTableTextBlock" xlink:to="us-gaap_FiniteLivedAndIndefiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedAndIndefiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived and Indefinite-Lived Intangible Assets Acquired as Part of Business Combination [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedAndIndefiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of preliminary fair value of intangible assets and estimated useful lives</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:to="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of property and equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:to="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Option, Activity [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of activity under the Plans</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotes2024And2025Member" xlink:label="cntm_ConvertibleNotes2024And2025Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotes2024And2025Member" xlink:to="cntm_ConvertibleNotes2024And2025Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotes2024And2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to 2024 and 2025 Convertible Notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotes2024And2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2024 and 2025 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotes2024And2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes 2024 and 2025</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_Amended2024ConvertibleNotesMember" xlink:label="cntm_Amended2024ConvertibleNotesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_Amended2024ConvertibleNotesMember" xlink:to="cntm_Amended2024ConvertibleNotesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_Amended2024ConvertibleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the entity's 2024 convertible notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_Amended2024ConvertibleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amended 2024 Convertible Notes [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_Amended2024ConvertibleNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amended 2024 Convertible Notes</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtConversionShareAdjustmentDerivativeLiabilityMember" xlink:label="cntm_DebtConversionShareAdjustmentDerivativeLiabilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtConversionShareAdjustmentDerivativeLiabilityMember" xlink:to="cntm_DebtConversionShareAdjustmentDerivativeLiabilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtConversionShareAdjustmentDerivativeLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to debt conversion share adjustment derivative liability.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtConversionShareAdjustmentDerivativeLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Conversion, Share Adjustment Derivative Liability [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtConversionShareAdjustmentDerivativeLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt conversion share adjustment obligations derivative liability</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StandbyEquityPurchaseAgreementDerivativeLiabilityMember" xlink:label="cntm_StandbyEquityPurchaseAgreementDerivativeLiabilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StandbyEquityPurchaseAgreementDerivativeLiabilityMember" xlink:to="cntm_StandbyEquityPurchaseAgreementDerivativeLiabilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StandbyEquityPurchaseAgreementDerivativeLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to standby equity purchase agreement derivative liability.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StandbyEquityPurchaseAgreementDerivativeLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Standby Equity Purchase Agreement Derivative Liability [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StandbyEquityPurchaseAgreementDerivativeLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SEPA Derivative Liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseCostTableTextBlock" xlink:label="us-gaap_LeaseCostTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LeaseCostTableTextBlock" xlink:to="us-gaap_LeaseCostTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LeaseCostTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lease, Cost [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LeaseCostTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of components of lease costs</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ScheduleOfWeightedAverageRemainingLeaseTermAndWeightedAverageDiscountRateTableTextBlock" xlink:label="cntm_ScheduleOfWeightedAverageRemainingLeaseTermAndWeightedAverageDiscountRateTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ScheduleOfWeightedAverageRemainingLeaseTermAndWeightedAverageDiscountRateTableTextBlock" xlink:to="cntm_ScheduleOfWeightedAverageRemainingLeaseTermAndWeightedAverageDiscountRateTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ScheduleOfWeightedAverageRemainingLeaseTermAndWeightedAverageDiscountRateTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular disclosure of information relating to weighted average remaining lease term and discount rates for all types of leases of a lessee.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ScheduleOfWeightedAverageRemainingLeaseTermAndWeightedAverageDiscountRateTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule Of Weighted Average Remaining Lease Term And Weighted Average Discount Rate [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ScheduleOfWeightedAverageRemainingLeaseTermAndWeightedAverageDiscountRateTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of weighted-average lease terms and discount rates</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LesseeOperatingLeaseFinanceLeaseLiabilityToBePaidMaturityTableTextBlock" xlink:label="cntm_LesseeOperatingLeaseFinanceLeaseLiabilityToBePaidMaturityTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LesseeOperatingLeaseFinanceLeaseLiabilityToBePaidMaturityTableTextBlock" xlink:to="cntm_LesseeOperatingLeaseFinanceLeaseLiabilityToBePaidMaturityTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LesseeOperatingLeaseFinanceLeaseLiabilityToBePaidMaturityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular disclosure of undiscounted cash flows of lessee's operating lease liability, finance lease liability, lease liability. Includes, but is not limited to, reconciliation of undiscounted cash flows to operating lease liability recognized in statement of financial position</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LesseeOperatingLeaseFinanceLeaseLiabilityToBePaidMaturityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Finance Lease Liability, to be Paid, Maturity [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LesseeOperatingLeaseFinanceLeaseLiabilityToBePaidMaturityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Summary of maturities of lease liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:label="us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:to="us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Liability, to be Paid, Maturity [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of maturities of finance lease liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xlink:label="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xlink:to="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Income before Income Tax, Domestic and Foreign [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of income before provision for (benefit from) income taxes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:label="us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:to="us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Components of Income Tax Expense (Benefit) [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of components of the provision for income taxes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:to="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Effective Income Tax Rate Reconciliation [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of reconciliation of the total income tax provision tax rate to the statutory federal income tax rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:label="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:to="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Deferred Tax Assets and Liabilities [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Deferred tax assets (liabilities)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputPriceVolatilityMember" xlink:label="us-gaap_MeasurementInputPriceVolatilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MeasurementInputPriceVolatilityMember" xlink:to="us-gaap_MeasurementInputPriceVolatilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MeasurementInputPriceVolatilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Price Volatility [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MeasurementInputPriceVolatilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Volatility</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConnectmBeforeBusinessCombinationMember" xlink:label="cntm_ConnectmBeforeBusinessCombinationMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConnectmBeforeBusinessCombinationMember" xlink:to="cntm_ConnectmBeforeBusinessCombinationMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConnectmBeforeBusinessCombinationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to connectm before business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConnectmBeforeBusinessCombinationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ConnectM Before Business Combination [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConnectmBeforeBusinessCombinationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ConnectM before business combination</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerMember" xlink:label="us-gaap_RevenueFromContractWithCustomerMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerMember" xlink:to="us-gaap_RevenueFromContractWithCustomerMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromContractWithCustomerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue from Contract with Customer Benchmark [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FirmwareEmbeddedInHardwareDevicesMember" xlink:label="cntm_FirmwareEmbeddedInHardwareDevicesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FirmwareEmbeddedInHardwareDevicesMember" xlink:to="cntm_FirmwareEmbeddedInHardwareDevicesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FirmwareEmbeddedInHardwareDevicesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to firmware embedded in the hardware devices.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FirmwareEmbeddedInHardwareDevicesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Firmware Embedded In Hardware Devices [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FirmwareEmbeddedInHardwareDevicesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Firmware embedded in hardware devices</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashUninsuredAmount" xlink:label="us-gaap_CashUninsuredAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashUninsuredAmount" xlink:to="us-gaap_CashUninsuredAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashUninsuredAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, Uninsured Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashUninsuredAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash accounts exceeding FDIC amounts</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CashUninsuredAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, uninsured amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashEquivalentsAtCarryingValue" xlink:label="us-gaap_CashEquivalentsAtCarryingValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashEquivalentsAtCarryingValue" xlink:to="us-gaap_CashEquivalentsAtCarryingValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashEquivalentsAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Equivalents, at Carrying Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashEquivalentsAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Allowance for Credit Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: allowance for credit losses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Allowance for credit losses</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CapitalizedSoftwareDevelopmentCosts" xlink:label="cntm_CapitalizedSoftwareDevelopmentCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CapitalizedSoftwareDevelopmentCosts" xlink:to="cntm_CapitalizedSoftwareDevelopmentCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CapitalizedSoftwareDevelopmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Costs incurred for development of computer software including capitalized costs of developing software for internal use.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CapitalizedSoftwareDevelopmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capitalized Software Development Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CapitalizedSoftwareDevelopmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total capitalized costs</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SoftwareSubscriptionsContactTerm" xlink:label="cntm_SoftwareSubscriptionsContactTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SoftwareSubscriptionsContactTerm" xlink:to="cntm_SoftwareSubscriptionsContactTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SoftwareSubscriptionsContactTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract term of software subscriptions, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SoftwareSubscriptionsContactTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Software Subscriptions, Contact Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SoftwareSubscriptionsContactTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Software Subscriptions - Contract term</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CommissionAndFinancingFeeExpenses" xlink:label="cntm_CommissionAndFinancingFeeExpenses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommissionAndFinancingFeeExpenses" xlink:to="cntm_CommissionAndFinancingFeeExpenses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommissionAndFinancingFeeExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expenses related to commission and financing fee expenses.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommissionAndFinancingFeeExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commission And Financing Fee Expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CommissionAndFinancingFeeExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commission and financing fee expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:label="us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:to="us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Remaining Lease Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining lease term</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeFinanceLeaseTermOfContract1" xlink:label="us-gaap_LesseeFinanceLeaseTermOfContract1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeFinanceLeaseTermOfContract1" xlink:to="us-gaap_LesseeFinanceLeaseTermOfContract1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeFinanceLeaseTermOfContract1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Finance Lease, Term of Contract</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeFinanceLeaseTermOfContract1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Initial term leases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseExistenceOfOptionToExtend" xlink:label="us-gaap_LesseeOperatingLeaseExistenceOfOptionToExtend" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseExistenceOfOptionToExtend" xlink:to="us-gaap_LesseeOperatingLeaseExistenceOfOptionToExtend_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseExistenceOfOptionToExtend_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Existence of Option to Extend [true false]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseExistenceOfOptionToExtend_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Renewal extending lease</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseRenewalTerm" xlink:label="us-gaap_LesseeOperatingLeaseRenewalTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseRenewalTerm" xlink:to="us-gaap_LesseeOperatingLeaseRenewalTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseRenewalTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Renewal Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseRenewalTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional renewal extending leases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignCurrencyTransactionGainLossRealizedAfterTax" xlink:label="us-gaap_ForeignCurrencyTransactionGainLossRealizedAfterTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ForeignCurrencyTransactionGainLossRealizedAfterTax" xlink:to="us-gaap_ForeignCurrencyTransactionGainLossRealizedAfterTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ForeignCurrencyTransactionGainLossRealizedAfterTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Realized Gain (Loss), Foreign Currency Transaction, after Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ForeignCurrencyTransactionGainLossRealizedAfterTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Realized foreign currency exchange gain (loss)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilityMeasurementInput" xlink:label="us-gaap_DerivativeLiabilityMeasurementInput" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeLiabilityMeasurementInput" xlink:to="us-gaap_DerivativeLiabilityMeasurementInput_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeLiabilityMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liability, Measurement Input</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeLiabilityMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdvertisingExpense" xlink:label="us-gaap_AdvertisingExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdvertisingExpense" xlink:to="us-gaap_AdvertisingExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdvertisingExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advertising Expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerRefundLiability" xlink:label="us-gaap_ContractWithCustomerRefundLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractWithCustomerRefundLiability" xlink:to="us-gaap_ContractWithCustomerRefundLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractWithCustomerRefundLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Refund Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ContractWithCustomerRefundLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">contract with customer, future estimated returns, amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DeterminationOfRelatedPartyThresholdPercentage" xlink:label="cntm_DeterminationOfRelatedPartyThresholdPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DeterminationOfRelatedPartyThresholdPercentage" xlink:to="cntm_DeterminationOfRelatedPartyThresholdPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DeterminationOfRelatedPartyThresholdPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the threshold percentage for determining the related party.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DeterminationOfRelatedPartyThresholdPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Determination Of Related Party, Threshold Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DeterminationOfRelatedPartyThresholdPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage for determining the related party</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProductWarrantyObligationLaborProvidedInstallationServicesTerm" xlink:label="cntm_ProductWarrantyObligationLaborProvidedInstallationServicesTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProductWarrantyObligationLaborProvidedInstallationServicesTerm" xlink:to="cntm_ProductWarrantyObligationLaborProvidedInstallationServicesTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProductWarrantyObligationLaborProvidedInstallationServicesTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term of warranty or group of similar warranties on labour provided installation services, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProductWarrantyObligationLaborProvidedInstallationServicesTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Product Warranty Obligation, Labor Provided Installation Services, Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProductWarrantyObligationLaborProvidedInstallationServicesTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Labor provided installation services, term</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProductWarrantyObligationStructuralDamageForInstallationServicesTerm" xlink:label="cntm_ProductWarrantyObligationStructuralDamageForInstallationServicesTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProductWarrantyObligationStructuralDamageForInstallationServicesTerm" xlink:to="cntm_ProductWarrantyObligationStructuralDamageForInstallationServicesTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProductWarrantyObligationStructuralDamageForInstallationServicesTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term of warranty or group of similar warranties on structural damage for certain installation services, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProductWarrantyObligationStructuralDamageForInstallationServicesTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Product Warranty Obligation, Structural Damage For Installation Services, Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProductWarrantyObligationStructuralDamageForInstallationServicesTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Structural damage for installation services, term</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StandardProductWarrantyAccrual" xlink:label="us-gaap_StandardProductWarrantyAccrual" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StandardProductWarrantyAccrual" xlink:to="us-gaap_StandardProductWarrantyAccrual_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StandardProductWarrantyAccrual_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Standard Product Warranty Accrual</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AccountsReceivableAfterAllowanceForCreditLossRollForward" xlink:label="cntm_AccountsReceivableAfterAllowanceForCreditLossRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AccountsReceivableAfterAllowanceForCreditLossRollForward" xlink:to="cntm_AccountsReceivableAfterAllowanceForCreditLossRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AccountsReceivableAfterAllowanceForCreditLossRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">No definition available.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AccountsReceivableAfterAllowanceForCreditLossRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, After Allowance For Credit Loss [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AccountsReceivableAfterAllowanceForCreditLossRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable, net roll forward</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableGrossCurrent" xlink:label="us-gaap_AccountsReceivableGrossCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableGrossCurrent" xlink:to="us-gaap_AccountsReceivableGrossCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableGrossCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, before Allowance for Credit Loss, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableGrossCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable, current</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableGross" xlink:label="us-gaap_AccountsReceivableGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableGross" xlink:to="us-gaap_AccountsReceivableGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, before Allowance for Credit Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AccountsReceivableGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total accounts receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableNet" xlink:label="us-gaap_AccountsReceivableNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableNet" xlink:to="us-gaap_AccountsReceivableNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, after Allowance for Credit Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AccountsReceivableNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total accounts receivable, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Allowance for Credit Loss [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Allowance for current expected credit losses roll forward</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Allowance for Credit Loss, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Allowance for expected credit losses, ending</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Allowance for expected credit losses, beginning</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Allowance for Credit Loss, Period Increase (Decrease)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period change for current expected credit losses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Allowance for Credit Loss, Writeoff</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Utilization of Expected credit loss</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryNetAbstract" xlink:label="us-gaap_InventoryNetAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryNetAbstract" xlink:to="us-gaap_InventoryNetAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryNetAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory, Net [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryNetAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory balances</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:to="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Lived Tangible Asset [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Lived Tangible Asset [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FurnitureAndFixturesMember" xlink:label="us-gaap_FurnitureAndFixturesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FurnitureAndFixturesMember" xlink:to="us-gaap_FurnitureAndFixturesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FurnitureAndFixturesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Furniture and Fixtures [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FurnitureAndFixturesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Furniture and Fixtures</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FurnitureAndFixturesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Furniture and fixtures</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MachineryAndEquipmentMember" xlink:label="us-gaap_MachineryAndEquipmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MachineryAndEquipmentMember" xlink:to="us-gaap_MachineryAndEquipmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MachineryAndEquipmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Machinery and Equipment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MachineryAndEquipmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Machinery and Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_MachineryAndEquipmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Machinery and equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VehiclesMember" xlink:label="us-gaap_VehiclesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VehiclesMember" xlink:to="us-gaap_VehiclesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_VehiclesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vehicles [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_VehiclesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vehicles</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BuildingImprovementsMember" xlink:label="us-gaap_BuildingImprovementsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BuildingImprovementsMember" xlink:to="us-gaap_BuildingImprovementsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BuildingImprovementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Building Improvements [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BuildingImprovementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property improvements</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BuildingMember" xlink:label="us-gaap_BuildingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BuildingMember" xlink:to="us-gaap_BuildingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BuildingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Building [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BuildingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Buildings</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BuildingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Building</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentLineItems" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">PROPERTY AND EQUIPMENT, NET</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:to="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment, Useful Life</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property plant and equipment useful lives</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SharesAuthorized" xlink:label="cntm_SharesAuthorized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SharesAuthorized" xlink:to="cntm_SharesAuthorized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The maximum number of shares permitted to be issued by an entity's charter and bylaws.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares Authorized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares authorized</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockConvertibleConversionRatio" xlink:label="us-gaap_PreferredStockConvertibleConversionRatio" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockConvertibleConversionRatio" xlink:to="us-gaap_PreferredStockConvertibleConversionRatio_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockConvertibleConversionRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Convertible, Conversion Ratio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockConvertibleConversionRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock, convertible, conversion ratio</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockConvertibleSharesIssuable" xlink:label="us-gaap_PreferredStockConvertibleSharesIssuable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockConvertibleSharesIssuable" xlink:to="us-gaap_PreferredStockConvertibleSharesIssuable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockConvertibleSharesIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Convertible, Shares Issuable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockConvertibleSharesIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares converted upon business combination</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharesIssuedPricePerShare" xlink:label="us-gaap_SharesIssuedPricePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharesIssuedPricePerShare" xlink:to="us-gaap_SharesIssuedPricePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares Issued, Price Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase price (in dollars per share)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase price, per unit</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessAcquisitionEquityInterestIssuedOrIssuableExchangeRatio" xlink:label="cntm_BusinessAcquisitionEquityInterestIssuedOrIssuableExchangeRatio" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessAcquisitionEquityInterestIssuedOrIssuableExchangeRatio" xlink:to="cntm_BusinessAcquisitionEquityInterestIssuedOrIssuableExchangeRatio_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessAcquisitionEquityInterestIssuedOrIssuableExchangeRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The exchange ratio used in connection with business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessAcquisitionEquityInterestIssuedOrIssuableExchangeRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Equity Interest Issued or Issuable, Exchange Ratio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessAcquisitionEquityInterestIssuedOrIssuableExchangeRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Exchange ratio</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WarrantsAndRightsOutstandingTerm" xlink:label="us-gaap_WarrantsAndRightsOutstandingTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WarrantsAndRightsOutstandingTerm" xlink:to="us-gaap_WarrantsAndRightsOutstandingTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WarrantsAndRightsOutstandingTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Warrants and Rights Outstanding, Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WarrantsAndRightsOutstandingTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Public warrants expiration term</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_WarrantsExpirationPeriod" xlink:label="cntm_WarrantsExpirationPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_WarrantsExpirationPeriod" xlink:to="cntm_WarrantsExpirationPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_WarrantsExpirationPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Warrants expiration period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_WarrantsExpirationPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Warrants Expiration Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_WarrantsExpirationPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Warrants expiration term</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRedeemedOrCalledDuringPeriodShares" xlink:label="us-gaap_StockRedeemedOrCalledDuringPeriodShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockRedeemedOrCalledDuringPeriodShares" xlink:to="us-gaap_StockRedeemedOrCalledDuringPeriodShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockRedeemedOrCalledDuringPeriodShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Redeemed or Called During Period, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_StockRedeemedOrCalledDuringPeriodShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Redeemed or Called During Period, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockRedeemedOrCalledDuringPeriodShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares redeemed</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:to="us-gaap_PaymentsForRepurchaseOfCommonStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments for Repurchase of Common Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of class a common stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodSharesRightIssues" xlink:label="cntm_StockIssuedDuringPeriodSharesRightIssues" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesRightIssues" xlink:to="cntm_StockIssuedDuringPeriodSharesRightIssues_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesRightIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of right shares issued during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesRightIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Right Issues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesRightIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Rights issued to shareholders</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_RightsConversionRatio" xlink:label="cntm_RightsConversionRatio" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RightsConversionRatio" xlink:to="cntm_RightsConversionRatio_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RightsConversionRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ratio applied to the conversion of rights issued.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RightsConversionRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Rights Conversion Ratio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RightsConversionRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Rights conversion ratio</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ForwardPurchaseAgreementSharesOutstanding" xlink:label="cntm_ForwardPurchaseAgreementSharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ForwardPurchaseAgreementSharesOutstanding" xlink:to="cntm_ForwardPurchaseAgreementSharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ForwardPurchaseAgreementSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares outstanding in connection with forward purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ForwardPurchaseAgreementSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Forward Purchase Agreement, Shares Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ForwardPurchaseAgreementSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares purchased by investor</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AdjustmentsToAdditionalPaidInCapitalNegativeEquityRecapitalization" xlink:label="cntm_AdjustmentsToAdditionalPaidInCapitalNegativeEquityRecapitalization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AdjustmentsToAdditionalPaidInCapitalNegativeEquityRecapitalization" xlink:to="cntm_AdjustmentsToAdditionalPaidInCapitalNegativeEquityRecapitalization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AdjustmentsToAdditionalPaidInCapitalNegativeEquityRecapitalization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase to additional paid-in capital (APIC) resulting from negative equity recapitalization.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AdjustmentsToAdditionalPaidInCapitalNegativeEquityRecapitalization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments To Additional Paid In Capital, Negative Equity Recapitalization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AdjustmentsToAdditionalPaidInCapitalNegativeEquityRecapitalization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Negative equity recapitalization</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CashAcquiredThroughReverseRecapitalization" xlink:label="cntm_CashAcquiredThroughReverseRecapitalization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CashAcquiredThroughReverseRecapitalization" xlink:to="cntm_CashAcquiredThroughReverseRecapitalization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CashAcquiredThroughReverseRecapitalization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of cash acquired through reverse recapitalization.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CashAcquiredThroughReverseRecapitalization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Acquired Through Reverse Recapitalization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CashAcquiredThroughReverseRecapitalization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash - MCAC's trust and cash (net of redemption)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfMergerRelatedCostsFinancingActivities" xlink:label="us-gaap_PaymentsOfMergerRelatedCostsFinancingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfMergerRelatedCostsFinancingActivities" xlink:to="us-gaap_PaymentsOfMergerRelatedCostsFinancingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfMergerRelatedCostsFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of Merger Related Costs, Financing Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsOfMergerRelatedCostsFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: transaction costs and advisory fees paid</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProceedsFromBusinessCombinationGross" xlink:label="cntm_ProceedsFromBusinessCombinationGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromBusinessCombinationGross" xlink:to="cntm_ProceedsFromBusinessCombinationGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromBusinessCombinationGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The cash inflow associated with the gross proceeds from business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromBusinessCombinationGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Business Combination, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="cntm_ProceedsFromBusinessCombinationGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Business Combination financing</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CommonStockSharesOutstandingAfterRedemption" xlink:label="cntm_CommonStockSharesOutstandingAfterRedemption" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommonStockSharesOutstandingAfterRedemption" xlink:to="cntm_CommonStockSharesOutstandingAfterRedemption_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommonStockSharesOutstandingAfterRedemption_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of common stock outstanding after redemption.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommonStockSharesOutstandingAfterRedemption_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares Outstanding After Redemption</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CommonStockSharesOutstandingAfterRedemption_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock of MCAC</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodFounderShares" xlink:label="cntm_StockIssuedDuringPeriodFounderShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodFounderShares" xlink:to="cntm_StockIssuedDuringPeriodFounderShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodFounderShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of founder shares issued during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodFounderShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Founder Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodFounderShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">MCAC founder shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationAndForwardPurchaseAgreementFinancingShares" xlink:label="cntm_BusinessCombinationAndForwardPurchaseAgreementFinancingShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationAndForwardPurchaseAgreementFinancingShares" xlink:to="cntm_BusinessCombinationAndForwardPurchaseAgreementFinancingShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationAndForwardPurchaseAgreementFinancingShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of financing shares issued as part of business combination and forward purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationAndForwardPurchaseAgreementFinancingShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination And Forward Purchase Agreement, Financing Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationAndForwardPurchaseAgreementFinancingShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination and forward purchase agreement financing shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockOfEntityEffectedForBusinessCombinationExchangeRatio" xlink:label="cntm_StockOfEntityEffectedForBusinessCombinationExchangeRatio" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockOfEntityEffectedForBusinessCombinationExchangeRatio" xlink:to="cntm_StockOfEntityEffectedForBusinessCombinationExchangeRatio_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockOfEntityEffectedForBusinessCombinationExchangeRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares effected as a result of business combination exchange ratio.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockOfEntityEffectedForBusinessCombinationExchangeRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Of Entity Effected For Business Combination Exchange Ratio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockOfEntityEffectedForBusinessCombinationExchangeRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Legacy ConnectM shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PreExchangeSharesMember" xlink:label="cntm_PreExchangeSharesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PreExchangeSharesMember" xlink:to="cntm_PreExchangeSharesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PreExchangeSharesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to shares before effected by business combination exchange ratio.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PreExchangeSharesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Pre Exchange Shares [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PreExchangeSharesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares effected for exchange ratio</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PostExchangeSharesMember" xlink:label="cntm_PostExchangeSharesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PostExchangeSharesMember" xlink:to="cntm_PostExchangeSharesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PostExchangeSharesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to shares effected for exchange ratio in business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PostExchangeSharesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Post Exchange Shares [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PostExchangeSharesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares effected for exchange ratio</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SeriesSeedConvertiblePreferredStockMember" xlink:label="cntm_SeriesSeedConvertiblePreferredStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SeriesSeedConvertiblePreferredStockMember" xlink:to="cntm_SeriesSeedConvertiblePreferredStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SeriesSeedConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Series Seed convertible preferred stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SeriesSeedConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series Seed Convertible Preferred Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SeriesSeedConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series Seed Convertible Preferred Shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SeriesSeed1ConvertiblePreferredStockMember" xlink:label="cntm_SeriesSeed1ConvertiblePreferredStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SeriesSeed1ConvertiblePreferredStockMember" xlink:to="cntm_SeriesSeed1ConvertiblePreferredStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SeriesSeed1ConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Series Seed-1 convertible preferred stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SeriesSeed1ConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series Seed-1 Convertible Preferred Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SeriesSeed1ConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series Seed-1 Convertible Preferred Shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_Seriesa1ConvertiblePreferredStockMember" xlink:label="cntm_Seriesa1ConvertiblePreferredStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_Seriesa1ConvertiblePreferredStockMember" xlink:to="cntm_Seriesa1ConvertiblePreferredStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_Seriesa1ConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Series A-1 convertible preferred stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_Seriesa1ConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SeriesA1 Convertible Preferred Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_Seriesa1ConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series A-1 Convertible Preferred Stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_Seriesb1ConvertiblePreferredStockMember" xlink:label="cntm_Seriesb1ConvertiblePreferredStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_Seriesb1ConvertiblePreferredStockMember" xlink:to="cntm_Seriesb1ConvertiblePreferredStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_Seriesb1ConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Series B-1 convertible preferred stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_Seriesb1ConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SeriesB1 Convertible Preferred Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_Seriesb1ConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series B-1 Convertible Preferred Stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_Seriesb2ConvertiblePreferredStockMember" xlink:label="cntm_Seriesb2ConvertiblePreferredStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_Seriesb2ConvertiblePreferredStockMember" xlink:to="cntm_Seriesb2ConvertiblePreferredStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_Seriesb2ConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Series B-2 convertible preferred stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_Seriesb2ConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SeriesB2 Convertible Preferred Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_Seriesb2ConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series B-2 Convertible Preferred Stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightAxis" xlink:label="us-gaap_ClassOfWarrantOrRightAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfWarrantOrRightAxis" xlink:to="us-gaap_ClassOfWarrantOrRightAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfWarrantOrRightAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Warrant or Right [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightDomain" xlink:label="us-gaap_ClassOfWarrantOrRightDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfWarrantOrRightDomain" xlink:to="us-gaap_ClassOfWarrantOrRightDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfWarrantOrRightDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Warrant or Right [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis" xlink:label="us-gaap_AwardTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AwardTypeAxis" xlink:to="us-gaap_AwardTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CommonStockSharesOutstandingRecapitalization" xlink:label="cntm_CommonStockSharesOutstandingRecapitalization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommonStockSharesOutstandingRecapitalization" xlink:to="cntm_CommonStockSharesOutstandingRecapitalization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommonStockSharesOutstandingRecapitalization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of common stock outstanding to which recapitalization is applied.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommonStockSharesOutstandingRecapitalization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Outstanding, Recapitalization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CommonStockSharesOutstandingRecapitalization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recapitalization applied to common stock outstanding</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockIssuedDuringPeriodSharesIssuedPriorToBusinessCombination" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedPriorToBusinessCombination" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockIssuedDuringPeriodSharesIssuedPriorToBusinessCombination" xlink:to="cntm_StockIssuedDuringPeriodSharesIssuedPriorToBusinessCombination_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedPriorToBusinessCombination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued to prior to closing of business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedPriorToBusinessCombination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares Issued Prior To Business Combination</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockIssuedDuringPeriodSharesIssuedPriorToBusinessCombination_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of Old ConnectM shares prior to closing of Business Combination</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PreferredStockSharesOutstandingRecapitalization" xlink:label="cntm_PreferredStockSharesOutstandingRecapitalization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PreferredStockSharesOutstandingRecapitalization" xlink:to="cntm_PreferredStockSharesOutstandingRecapitalization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PreferredStockSharesOutstandingRecapitalization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of preferred stock outstanding to which recapitalization is applied.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PreferredStockSharesOutstandingRecapitalization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Shares Outstanding, Recapitalization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PreferredStockSharesOutstandingRecapitalization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recapitalization applied to preferred stock outstanding</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:to="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Capital Shares Reserved for Future Issuance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total share reserve</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionAxis" xlink:label="us-gaap_AssetAcquisitionAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionAxis" xlink:to="us-gaap_AssetAcquisitionAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionDomain" xlink:label="us-gaap_AssetAcquisitionDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionDomain" xlink:to="us-gaap_AssetAcquisitionDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuableNumberOfShares" xlink:label="cntm_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuableNumberOfShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuableNumberOfShares" xlink:to="cntm_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuableNumberOfShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuableNumberOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of equity interests issued or issuable as part of consideration transferred in asset acquisition.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuableNumberOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Consideration Transferred, Equity Interest Issued and Issuable, Number of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuableNumberOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset acquisition, number of shares</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharePrice" xlink:label="us-gaap_SharePrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharePrice" xlink:to="us-gaap_SharePrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share price per unit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuable" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuable" xlink:to="us-gaap_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Consideration Transferred, Equity Interest Issued and Issuable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireProductiveAssets" xlink:label="us-gaap_PaymentsToAcquireProductiveAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireProductiveAssets" xlink:to="us-gaap_PaymentsToAcquireProductiveAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireProductiveAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Productive Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PaymentsToAcquireProductiveAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset acquisition, cash paid</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsNet" xlink:label="us-gaap_AssetsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsNet" xlink:to="us-gaap_AssetsNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total assets acquired</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:to="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquired Finite-Lived Intangible Assets, Weighted Average Useful Life</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Identified intangible asset, Useful life</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsidiary, Ownership Percentage, Noncontrolling Owner</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of voting interest held by NCI</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationAcquisitionOfLessThan100PercentNoncontrollingInterestFairValue" xlink:label="us-gaap_BusinessCombinationAcquisitionOfLessThan100PercentNoncontrollingInterestFairValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationAcquisitionOfLessThan100PercentNoncontrollingInterestFairValue" xlink:to="us-gaap_BusinessCombinationAcquisitionOfLessThan100PercentNoncontrollingInterestFairValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationAcquisitionOfLessThan100PercentNoncontrollingInterestFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Acquisition of Less than 100 Percent, Noncontrolling Interest, Fair Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationAcquisitionOfLessThan100PercentNoncontrollingInterestFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-controlling interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:to="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Equity Interests Issued and Issuable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration transferred, equity interests issued and issuable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of shares issued</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationConsiderationTransferredPromissoryNoteAssumed" xlink:label="cntm_BusinessCombinationConsiderationTransferredPromissoryNoteAssumed" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationConsiderationTransferredPromissoryNoteAssumed" xlink:to="cntm_BusinessCombinationConsiderationTransferredPromissoryNoteAssumed_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationConsiderationTransferredPromissoryNoteAssumed_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of  promissory note issued by the acquirer as part of consideration transferred in a business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationConsiderationTransferredPromissoryNoteAssumed_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Promissory Note Assumed</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationConsiderationTransferredPromissoryNoteAssumed_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination, value of promissory considered</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationConsiderationTransferred1" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationConsiderationTransferred1" xlink:to="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total purchase consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total consideration</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total assets acquired</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredTaxLiabilities" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredTaxLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Liabilities, Accounts Payable</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt, net of current portion</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Liabilities</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total liabilities assumed</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net assets acquired</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AirTempServicesCoIncMember" xlink:label="cntm_AirTempServicesCoIncMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CerMicrogridsPrivateLimitedMember" xlink:label="cntm_CerMicrogridsPrivateLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ThresholdPeriodForDelistingFromClosing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the threshold period for delisting from NASDAQ of closing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ThresholdPeriodForDelistingFromClosing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold Period for Delisting from Closing</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ThresholdPeriodForDelistingFromClosing_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold period for delisting</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationContingentConsiderationTransferredEquityInterestShareIssuedNumberOfShares" xlink:label="cntm_BusinessCombinationContingentConsiderationTransferredEquityInterestShareIssuedNumberOfShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationContingentConsiderationTransferredEquityInterestShareIssuedNumberOfShares" xlink:to="cntm_BusinessCombinationContingentConsiderationTransferredEquityInterestShareIssuedNumberOfShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationContingentConsiderationTransferredEquityInterestShareIssuedNumberOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of equity interest issued or issuable by acquirer as part of  contingent consideration transferred in business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationContingentConsiderationTransferredEquityInterestShareIssuedNumberOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration Transferred, Equity Interest, Share Issued, Number of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationContingentConsiderationTransferredEquityInterestShareIssuedNumberOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingently issuable equity shares</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionSharePrice" xlink:label="us-gaap_BusinessAcquisitionSharePrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionSharePrice" xlink:to="us-gaap_BusinessAcquisitionSharePrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionSharePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Share Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionSharePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share price of acquisition (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationContingentConsiderationTransferred" xlink:label="cntm_BusinessCombinationContingentConsiderationTransferred" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationContingentConsiderationTransferred" xlink:to="cntm_BusinessCombinationContingentConsiderationTransferred_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationContingentConsiderationTransferred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of contingent consideration transferred.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationContingentConsiderationTransferred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration Transferred</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationContingentConsiderationTransferred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_BusinessCombinationContingentConsiderationTransferred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration - IREDA</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationConsiderationTransferredFairValueOfSharesIssued" xlink:label="cntm_BusinessCombinationConsiderationTransferredFairValueOfSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationConsiderationTransferredFairValueOfSharesIssued" xlink:to="cntm_BusinessCombinationConsiderationTransferredFairValueOfSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationConsiderationTransferredFairValueOfSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of equity interests of the acquirer measured at fair value, including shares issued or issuable, recognized as consideration transferred in a business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationConsiderationTransferredFairValueOfSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Fair Value of Shares Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="cntm_BusinessCombinationConsiderationTransferredFairValueOfSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total fair value of shares issues</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationSettlementOfPreexistingRelationshipAmount" xlink:label="cntm_BusinessCombinationSettlementOfPreexistingRelationshipAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationSettlementOfPreexistingRelationshipAmount" xlink:to="cntm_BusinessCombinationSettlementOfPreexistingRelationshipAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationSettlementOfPreexistingRelationshipAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount recognized for the settlement of a preexisting relationship between the acquirer and the acquiree in a business combination. This amount is accounted for separately from the business combination and is not part of the consideration transferred.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationSettlementOfPreexistingRelationshipAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Settlement of Preexisting Relationship, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationSettlementOfPreexistingRelationshipAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement of preexisting relationship (accounts receivable / payable)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessAcquisitionNumberOfSubsidiariesOfAcquireeAcquired" xlink:label="cntm_BusinessAcquisitionNumberOfSubsidiariesOfAcquireeAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessAcquisitionNumberOfSubsidiariesOfAcquireeAcquired" xlink:to="cntm_BusinessAcquisitionNumberOfSubsidiariesOfAcquireeAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessAcquisitionNumberOfSubsidiariesOfAcquireeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of subsidiaries of the acquiree acquired during the period under the business combination transaction.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessAcquisitionNumberOfSubsidiariesOfAcquireeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Number Of Subsidiaries Of Acquiree Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessAcquisitionNumberOfSubsidiariesOfAcquireeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of subsidiaries acquired</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessAcquisitionNumberOfJointVentureOfAcquireeAcquired" xlink:label="cntm_BusinessAcquisitionNumberOfJointVentureOfAcquireeAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessAcquisitionNumberOfJointVentureOfAcquireeAcquired" xlink:to="cntm_BusinessAcquisitionNumberOfJointVentureOfAcquireeAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessAcquisitionNumberOfJointVentureOfAcquireeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of joint ventures of the acquiree acquired during the period under the business combination transaction.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessAcquisitionNumberOfJointVentureOfAcquireeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Number Of Joint Venture Of Acquiree Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessAcquisitionNumberOfJointVentureOfAcquireeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of joint venture</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessAcquisitionCommittedCapitalInfusionForEquityOfAcquiree" xlink:label="cntm_BusinessAcquisitionCommittedCapitalInfusionForEquityOfAcquiree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessAcquisitionCommittedCapitalInfusionForEquityOfAcquiree" xlink:to="cntm_BusinessAcquisitionCommittedCapitalInfusionForEquityOfAcquiree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessAcquisitionCommittedCapitalInfusionForEquityOfAcquiree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of capital committed to be infused by the acquirer for exchange of equity of the acquiree in a business combination transaction.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessAcquisitionCommittedCapitalInfusionForEquityOfAcquiree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Committed Capital Infusion For Equity Of Acquiree</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessAcquisitionCommittedCapitalInfusionForEquityOfAcquiree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Committed capital to be provided</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessAcquisitionAggregatePortionOfCommittedCapitalFunded" xlink:label="cntm_BusinessAcquisitionAggregatePortionOfCommittedCapitalFunded" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessAcquisitionAggregatePortionOfCommittedCapitalFunded" xlink:to="cntm_BusinessAcquisitionAggregatePortionOfCommittedCapitalFunded_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessAcquisitionAggregatePortionOfCommittedCapitalFunded_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate portion of committed capital funded as of the balance sheet date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessAcquisitionAggregatePortionOfCommittedCapitalFunded_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Aggregate Portion Of Committed Capital Funded</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessAcquisitionAggregatePortionOfCommittedCapitalFunded_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate portion funded</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationBargainPurchaseGainRecognizedBeforeFairValueAdjustmentAmount" xlink:label="cntm_BusinessCombinationBargainPurchaseGainRecognizedBeforeFairValueAdjustmentAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationBargainPurchaseGainRecognizedBeforeFairValueAdjustmentAmount" xlink:to="cntm_BusinessCombinationBargainPurchaseGainRecognizedBeforeFairValueAdjustmentAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationBargainPurchaseGainRecognizedBeforeFairValueAdjustmentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">In a business combination before fair value adjustment in which the amount of net identifiable assets acquired and liabilities assumed exceeds the aggregate consideration transferred or to be transferred (as defined), this element represents the amount of gain recognized by the entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationBargainPurchaseGainRecognizedBeforeFairValueAdjustmentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Bargain Purchase, Gain Recognized, Before Fair Value Adjustment, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationBargainPurchaseGainRecognizedBeforeFairValueAdjustmentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bargain purchase gain</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationLatePaymentSurchargeFeesPercent" xlink:label="cntm_BusinessCombinationLatePaymentSurchargeFeesPercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationLatePaymentSurchargeFeesPercent" xlink:to="cntm_BusinessCombinationLatePaymentSurchargeFeesPercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationLatePaymentSurchargeFeesPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of surcharge fees levied on late payments of consideration in business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationLatePaymentSurchargeFeesPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Late Payment, Surcharge Fees, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationLatePaymentSurchargeFeesPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Late payment, surcharge fees, percent</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationDiscountRate" xlink:label="cntm_BusinessCombinationDiscountRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationDiscountRate" xlink:to="cntm_BusinessCombinationDiscountRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationDiscountRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The estimated assetspecific discount rate used in the business combination to determine the asset fair value based on net projected revenues.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationDiscountRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Discount Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationDiscountRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination, discount rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TrademarksMember" xlink:label="us-gaap_TrademarksMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TrademarksMember" xlink:to="us-gaap_TrademarksMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TrademarksMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Trademarks [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TrademarksMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Trademark</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract" xlink:to="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Assets [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccountsReceivables" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccountsReceivables" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccountsReceivables" xlink:to="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccountsReceivables_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccountsReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount due from customers or clients for goods or services, including trade receivables, that have been delivered or sold in the normal course of business, acquired at the acquisition date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccountsReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Accounts Receivables</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccountsReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPrepaidExpense" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPrepaidExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPrepaidExpense" xlink:to="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPrepaidExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPrepaidExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of asset related to consideration paid in advance for costs that provide economic benefits in future periods acquired at the acquisition date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPrepaidExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Prepaid Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPrepaidExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepaid expenses and other current assets</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRightOfUseAsset" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRightOfUseAsset" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of right of use asset acquired at the acquisition date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Right Of Use Asset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-use asset - operating lease</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles" xlink:to="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Finite-Lived Intangibles</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of identifiable intangible assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract" xlink:to="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Liabilities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherCurrentLiabilities" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherCurrentLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherCurrentLiabilities" xlink:to="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherCurrentLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherCurrentLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of liabilities incurred and assumed at the accrued expenses and other current liabilities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherCurrentLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed Accrued Expenses And Other Current Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherCurrentLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued expenses and other current liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDebtNetOfDebtDiscount" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDebtNetOfDebtDiscount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDebtNetOfDebtDiscount" xlink:to="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDebtNetOfDebtDiscount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDebtNetOfDebtDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of liabilities incurred and assumed at the debt, net of debt discount.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDebtNetOfDebtDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed Debt Net Of Debt Discount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDebtNetOfDebtDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt, net of debt discount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedContractLiabilities" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedContractLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedContractLiabilities" xlink:to="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedContractLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedContractLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of liabilities incurred and assumed at the contract.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedContractLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed Contract Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedContractLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCapitalLeaseObligation" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCapitalLeaseObligation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCapitalLeaseObligation" xlink:to="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCapitalLeaseObligation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCapitalLeaseObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Asset Acquired and Liability Assumed, Lease Obligation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCapitalLeaseObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred" xlink:to="us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Liabilities Incurred</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration at fair value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement of liabilities with NCLT plan</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationDeferredConsideration" xlink:label="cntm_BusinessCombinationDeferredConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationDeferredConsideration" xlink:to="cntm_BusinessCombinationDeferredConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationDeferredConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of deferred consideration transferred in business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationDeferredConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Deferred Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationDeferredConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred consideration</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationPresentValueOfDeferredConsideration" xlink:label="cntm_BusinessCombinationPresentValueOfDeferredConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationPresentValueOfDeferredConsideration" xlink:to="cntm_BusinessCombinationPresentValueOfDeferredConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationPresentValueOfDeferredConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of present value of deferred consideration transferred in business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationPresentValueOfDeferredConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Present Value of Deferred Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationPresentValueOfDeferredConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Present value of deferred consideration</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationConsiderationTransferredCash" xlink:label="cntm_BusinessCombinationConsiderationTransferredCash" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationConsiderationTransferredCash" xlink:to="cntm_BusinessCombinationConsiderationTransferredCash_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationConsiderationTransferredCash_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the amount of cash as part of consideration transferred in a business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationConsiderationTransferredCash_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Cash</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationConsiderationTransferredCash_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationConsiderationTransferredNonControllingInterest" xlink:label="cntm_BusinessCombinationConsiderationTransferredNonControllingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationConsiderationTransferredNonControllingInterest" xlink:to="cntm_BusinessCombinationConsiderationTransferredNonControllingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationConsiderationTransferredNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the amount of non-controlling interest consideration transferred as part of business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationConsiderationTransferredNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Non-controlling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationConsiderationTransferredNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling interest at fair value</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationConsiderationTransferredNotesReceivableSettled" xlink:label="cntm_BusinessCombinationConsiderationTransferredNotesReceivableSettled" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationConsiderationTransferredNotesReceivableSettled" xlink:to="cntm_BusinessCombinationConsiderationTransferredNotesReceivableSettled_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationConsiderationTransferredNotesReceivableSettled_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of notes receivable assets netted off by the acquirer as part of consideration transferred in a business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationConsiderationTransferredNotesReceivableSettled_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Notes Receivable Settled</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationConsiderationTransferredNotesReceivableSettled_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement of note receivable from GEG</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationConsiderationTransferredAccountsReceivableSettled" xlink:label="cntm_BusinessCombinationConsiderationTransferredAccountsReceivableSettled" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationConsiderationTransferredAccountsReceivableSettled" xlink:to="cntm_BusinessCombinationConsiderationTransferredAccountsReceivableSettled_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationConsiderationTransferredAccountsReceivableSettled_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of accounts receivable assets netted off by the acquirer as part of consideration transferred in a business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationConsiderationTransferredAccountsReceivableSettled_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Accounts Receivable Settled</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationConsiderationTransferredAccountsReceivableSettled_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement of accounts receivable from GEG</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DeliveryCircleLlcMember" xlink:label="cntm_DeliveryCircleLlcMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DeliveryCircleLlcMember" xlink:to="cntm_DeliveryCircleLlcMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DeliveryCircleLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to DeliveryCircle, LLC</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DeliveryCircleLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Delivery Circle LLC [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DeliveryCircleLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DeliveryCircle, LLC</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccruedExpensesAndOther" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccruedExpensesAndOther" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccruedExpensesAndOther" xlink:to="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccruedExpensesAndOther_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccruedExpensesAndOther_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of liabilities incurred for accrued expenses and other current liabilities, assumed at the acquisition date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccruedExpensesAndOther_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Liabilities, Accrued Expenses And Other</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccruedExpensesAndOther_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued expenses and other current liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalUnitsByClassAxis" xlink:label="us-gaap_CapitalUnitsByClassAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CapitalUnitsByClassAxis" xlink:to="us-gaap_CapitalUnitsByClassAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CapitalUnitsByClassAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital Units by Class [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalUnitClassDomain" xlink:label="us-gaap_CapitalUnitClassDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CapitalUnitClassDomain" xlink:to="us-gaap_CapitalUnitClassDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CapitalUnitClassDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital Unit, Class [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalUnitClassAMember" xlink:label="us-gaap_CapitalUnitClassAMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CapitalUnitClassAMember" xlink:to="us-gaap_CapitalUnitClassAMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CapitalUnitClassAMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital Unit, Class A [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CapitalUnitClassAMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class A Units</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CapitalUnitClassPMember" xlink:label="cntm_CapitalUnitClassPMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CapitalUnitClassPMember" xlink:to="cntm_CapitalUnitClassPMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CapitalUnitClassPMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class P of capital units, which are a type of ownership interest in a corporation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CapitalUnitClassPMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital Unit, Class P [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CapitalUnitClassPMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class P Units</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CapitalUnitSeriesMember" xlink:label="cntm_CapitalUnitSeriesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CapitalUnitSeriesMember" xlink:to="cntm_CapitalUnitSeriesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CapitalUnitSeriesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series A of capital units, which are a type of ownership interest in a corporation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CapitalUnitSeriesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital Unit, Series A [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CapitalUnitSeriesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series A Units</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_January2025NoteMember" xlink:label="cntm_January2025NoteMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_January2025NoteMember" xlink:to="cntm_January2025NoteMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_January2025NoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to January 2025 notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_January2025NoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">January 2025 Note [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_January2025NoteMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">January 2025 Note</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_TitleOfIndividualAxis" xlink:label="srt_TitleOfIndividualAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_TitleOfIndividualAxis" xlink:to="srt_TitleOfIndividualAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_TitleOfIndividualAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Title and Position [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:label="srt_TitleOfIndividualWithRelationshipToEntityDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:to="srt_TitleOfIndividualWithRelationshipToEntityDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_TitleOfIndividualWithRelationshipToEntityDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Title and Position [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GregKendallMember" xlink:label="cntm_GregKendallMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GregKendallMember" xlink:to="cntm_GregKendallMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GregKendallMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represent information pertaining to Greg Kendall.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GregKendallMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Greg Kendall [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GregKendallMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Greg Kendall</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessAcquisitionMembershipInterestsAcquired" xlink:label="cntm_BusinessAcquisitionMembershipInterestsAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessAcquisitionMembershipInterestsAcquired" xlink:to="cntm_BusinessAcquisitionMembershipInterestsAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessAcquisitionMembershipInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of membership interests acquired by the company.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessAcquisitionMembershipInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Membership Interests Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessAcquisitionMembershipInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of membership interests acquired</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessAcquisitionPercentageOfEquityInterestsAcquired" xlink:label="cntm_BusinessAcquisitionPercentageOfEquityInterestsAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessAcquisitionPercentageOfEquityInterestsAcquired" xlink:to="cntm_BusinessAcquisitionPercentageOfEquityInterestsAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessAcquisitionPercentageOfEquityInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of voting equity interests acquired at the acquisition date in the business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessAcquisitionPercentageOfEquityInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Percentage of Equity Interests Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessAcquisitionPercentageOfEquityInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of equity interests acquired</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfVotingMembersRightToAppoint" xlink:label="cntm_NumberOfVotingMembersRightToAppoint" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfVotingMembersRightToAppoint" xlink:to="cntm_NumberOfVotingMembersRightToAppoint_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfVotingMembersRightToAppoint_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of voting members that can be appointed to the board of directors by the entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfVotingMembersRightToAppoint_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Voting Members, Right To Appoint</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfVotingMembersRightToAppoint_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of voting members</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_TotalNumberOfVotingMembersOfBoard" xlink:label="cntm_TotalNumberOfVotingMembersOfBoard" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_TotalNumberOfVotingMembersOfBoard" xlink:to="cntm_TotalNumberOfVotingMembersOfBoard_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_TotalNumberOfVotingMembersOfBoard_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total number of voting members of the board of directors of the entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_TotalNumberOfVotingMembersOfBoard_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total Number Of Voting Members Of The Board</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_TotalNumberOfVotingMembersOfBoard_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total number of voting members</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessAcquisitionThresholdRevenueGrowthPercentageConsideredForContingentPayment" xlink:label="cntm_BusinessAcquisitionThresholdRevenueGrowthPercentageConsideredForContingentPayment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessAcquisitionThresholdRevenueGrowthPercentageConsideredForContingentPayment" xlink:to="cntm_BusinessAcquisitionThresholdRevenueGrowthPercentageConsideredForContingentPayment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessAcquisitionThresholdRevenueGrowthPercentageConsideredForContingentPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue growth percentage of the applicable measurement year considered for the contingent payment, under the business combination transaction.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessAcquisitionThresholdRevenueGrowthPercentageConsideredForContingentPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Threshold Revenue Growth Percentage, Considered For Contingent Payment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessAcquisitionThresholdRevenueGrowthPercentageConsideredForContingentPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue growth percentage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationUnpaidCashConsiderationPayable" xlink:label="cntm_BusinessCombinationUnpaidCashConsiderationPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationUnpaidCashConsiderationPayable" xlink:to="cntm_BusinessCombinationUnpaidCashConsiderationPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationUnpaidCashConsiderationPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the amount of unpaid cash consideration payable for business combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationUnpaidCashConsiderationPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Unpaid Cash Consideration Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationUnpaidCashConsiderationPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unpaid cash consideration payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentFaceAmountInterest" xlink:label="cntm_DebtInstrumentFaceAmountInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentFaceAmountInterest" xlink:to="cntm_DebtInstrumentFaceAmountInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentFaceAmountInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Face (par) amount of interest amount of debt instrument at time of issuance.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentFaceAmountInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Face Amount, Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentFaceAmountInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument - interest</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentFaceAmountPrincipal" xlink:label="cntm_DebtInstrumentFaceAmountPrincipal" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentFaceAmountPrincipal" xlink:to="cntm_DebtInstrumentFaceAmountPrincipal_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentFaceAmountPrincipal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Face (par) amount of principal amount of debt instrument at time of issuance.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentFaceAmountPrincipal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Face Amount, Principal</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentFaceAmountPrincipal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument - principal</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentDebtDefaultInterestRate" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentDebtDefaultInterestRate" xlink:to="cntm_DebtInstrumentDebtDefaultInterestRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contractual interest rate for funds borrowed, under the debt agreement in the event of default.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Debt Default, Interest Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument - interest rate in case of default</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_DebtInstrumentDebtDefaultInterestRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument - interest rate in case of default (in percentage)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:to="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Periodic Payment, Principal</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument periodic payment principal</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentPeriodicPaymentInterest" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentPeriodicPaymentInterest" xlink:to="us-gaap_DebtInstrumentPeriodicPaymentInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Periodic Payment, Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LegalFees" xlink:label="us-gaap_LegalFees" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LegalFees" xlink:to="us-gaap_LegalFees_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LegalFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Legal Fees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LegalFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Attomey"s fees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_LegalFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Legal fees</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage" xlink:label="us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage" xlink:to="us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Step Acquisition, Equity Interest in Acquiree, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of equity interest in acquiree</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessAcquisitionEquityInterestIssuedOrIssuableNumberOfCommonShares" xlink:label="cntm_BusinessAcquisitionEquityInterestIssuedOrIssuableNumberOfCommonShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessAcquisitionEquityInterestIssuedOrIssuableNumberOfCommonShares" xlink:to="cntm_BusinessAcquisitionEquityInterestIssuedOrIssuableNumberOfCommonShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessAcquisitionEquityInterestIssuedOrIssuableNumberOfCommonShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of equity interests issued or issuable to acquire entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessAcquisitionEquityInterestIssuedOrIssuableNumberOfCommonShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Equity Interest Issued or Issuable, Number of Common Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessAcquisitionEquityInterestIssuedOrIssuableNumberOfCommonShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of common shares issued as merger consideration</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MinimumOwnershipPercentageOnEachAdvanceOfTotalSharesOutstanding" xlink:label="cntm_MinimumOwnershipPercentageOnEachAdvanceOfTotalSharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MinimumOwnershipPercentageOnEachAdvanceOfTotalSharesOutstanding" xlink:to="cntm_MinimumOwnershipPercentageOnEachAdvanceOfTotalSharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MinimumOwnershipPercentageOnEachAdvanceOfTotalSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum percentage of ownership to be permitted under each advance of total shares outstanding.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MinimumOwnershipPercentageOnEachAdvanceOfTotalSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum Ownership Percentage On Each Advance Of Total Shares Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MinimumOwnershipPercentageOnEachAdvanceOfTotalSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum percentage of ownership</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xlink:label="us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xlink:to="us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Pro Forma Information, Revenue of Acquiree since Acquisition Date, Actual</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue of acquiree since acquisition date, actuals</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:label="us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:to="us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Acquiree's Earnings (Loss) since Acquisition Date, Actual</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss of acquiree since acquisition date, actuals</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentForbearanceFee" xlink:label="cntm_DebtInstrumentForbearanceFee" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentForbearanceFee" xlink:to="cntm_DebtInstrumentForbearanceFee_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentForbearanceFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of forbearance fee expense incurred for extension of existing debt outstanding.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentForbearanceFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Forbearance Fee</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentForbearanceFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Forbearance fee</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessAcquisitionThresholdEarningsBeforeInterestTaxDepreciationAndAmortizationPercentageConsideredForContingentPayment" xlink:label="cntm_BusinessAcquisitionThresholdEarningsBeforeInterestTaxDepreciationAndAmortizationPercentageConsideredForContingentPayment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessAcquisitionThresholdEarningsBeforeInterestTaxDepreciationAndAmortizationPercentageConsideredForContingentPayment" xlink:to="cntm_BusinessAcquisitionThresholdEarningsBeforeInterestTaxDepreciationAndAmortizationPercentageConsideredForContingentPayment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessAcquisitionThresholdEarningsBeforeInterestTaxDepreciationAndAmortizationPercentageConsideredForContingentPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings before interest, tax, depreciation and amortization percentage of applicable measurement year considered for contingent payment, under the business combination transaction.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessAcquisitionThresholdEarningsBeforeInterestTaxDepreciationAndAmortizationPercentageConsideredForContingentPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Threshold Earnings Before Interest, Tax, Depreciation And Amortization Percentage, Considered For Contingent Payment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessAcquisitionThresholdEarningsBeforeInterestTaxDepreciationAndAmortizationPercentageConsideredForContingentPayment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Annually paid</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillRollForward" xlink:label="us-gaap_GoodwillRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillRollForward" xlink:to="us-gaap_GoodwillRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GoodwillRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAcquiredDuringPeriod" xlink:label="us-gaap_GoodwillAcquiredDuringPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAcquiredDuringPeriod" xlink:to="us-gaap_GoodwillAcquiredDuringPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillAcquiredDuringPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill, Acquired During Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GoodwillAcquiredDuringPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisitions</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillImpairmentLoss" xlink:label="us-gaap_GoodwillImpairmentLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillImpairmentLoss" xlink:to="us-gaap_GoodwillImpairmentLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillImpairmentLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill, Impairment Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_GoodwillImpairmentLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GoodwillImpairmentLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment of goodwill</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillImpairmentLossStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xlink:label="us-gaap_GoodwillImpairmentLossStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillImpairmentLossStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xlink:to="us-gaap_GoodwillImpairmentLossStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillImpairmentLossStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill, Impairment Loss, Statement of Income or Comprehensive Income [Extensible Enumeration]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LandMember" xlink:label="us-gaap_LandMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LandMember" xlink:to="us-gaap_LandMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LandMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Land [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LandMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Land</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentGross" xlink:label="us-gaap_PropertyPlantAndEquipmentGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentGross" xlink:to="us-gaap_PropertyPlantAndEquipmentGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property and Equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:to="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: Accumulated Depreciation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Depreciation" xlink:label="us-gaap_Depreciation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Depreciation" xlink:to="us-gaap_Depreciation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Depreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Depreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentIncreaseDecreaseForPeriodNet" xlink:label="us-gaap_DebtInstrumentIncreaseDecreaseForPeriodNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentIncreaseDecreaseForPeriodNet" xlink:to="us-gaap_DebtInstrumentIncreaseDecreaseForPeriodNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentIncreaseDecreaseForPeriodNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Increase (Decrease), Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentIncreaseDecreaseForPeriodNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated fair value</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AfterSecondTrancheOfReceiptOfAdvancesMember" xlink:label="cntm_AfterSecondTrancheOfReceiptOfAdvancesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AfterSecondTrancheOfReceiptOfAdvancesMember" xlink:to="cntm_AfterSecondTrancheOfReceiptOfAdvancesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AfterSecondTrancheOfReceiptOfAdvancesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to after second tranche of receipt of advances.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AfterSecondTrancheOfReceiptOfAdvancesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">After Second Tranche Of Receipt Of Advances [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AfterSecondTrancheOfReceiptOfAdvancesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">After Second Tranche Of Receipt Of Advances</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:to="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Extinguishment of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on extinguishment of debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on extinguishment of debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (loss) on extinguishment of debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PaycheckProtectionProgramMember" xlink:label="cntm_PaycheckProtectionProgramMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaycheckProtectionProgramMember" xlink:to="cntm_PaycheckProtectionProgramMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaycheckProtectionProgramMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to paycheck protection program.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaycheckProtectionProgramMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Paycheck Protection Program [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PaycheckProtectionProgramMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Paycheck Protection Program Loans</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentNumberOfConversionAgreements" xlink:label="cntm_DebtInstrumentNumberOfConversionAgreements" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentNumberOfConversionAgreements" xlink:to="cntm_DebtInstrumentNumberOfConversionAgreements_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentNumberOfConversionAgreements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of debt conversion agreements entered into by the entity during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentNumberOfConversionAgreements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Number Of Conversion Agreements</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentNumberOfConversionAgreements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of conversion agreements</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfLendersExceedingThresholdPercentageRelatedParty" xlink:label="cntm_NumberOfLendersExceedingThresholdPercentageRelatedParty" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfLendersExceedingThresholdPercentageRelatedParty" xlink:to="cntm_NumberOfLendersExceedingThresholdPercentageRelatedParty_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfLendersExceedingThresholdPercentageRelatedParty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the number of lenders exceeding the threshold percentage to be considered as related party.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfLendersExceedingThresholdPercentageRelatedParty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Lenders Exceeding Threshold Percentage, Related Party</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfLendersExceedingThresholdPercentageRelatedParty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of lenders exceeding the threshold percentage to be considered as related party</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentNumberOfAgreements" xlink:label="cntm_DebtInstrumentNumberOfAgreements" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentNumberOfAgreements" xlink:to="cntm_DebtInstrumentNumberOfAgreements_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentNumberOfAgreements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of debt instrument agreements entered into by the entity during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentNumberOfAgreements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Number Of Agreements</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentNumberOfAgreements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of debt instrument agreements</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentAdditionalDebtNumber" xlink:label="cntm_DebtInstrumentAdditionalDebtNumber" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentAdditionalDebtNumber" xlink:to="cntm_DebtInstrumentAdditionalDebtNumber_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentAdditionalDebtNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of additional debt issued during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentAdditionalDebtNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Additional Debt, Number</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentAdditionalDebtNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of additonal debt</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfPromissoryNoteAgreementsEntered" xlink:label="cntm_NumberOfPromissoryNoteAgreementsEntered" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfPromissoryNoteAgreementsEntered" xlink:to="cntm_NumberOfPromissoryNoteAgreementsEntered_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfPromissoryNoteAgreementsEntered_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of promissory note agreements entered into by the company.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfPromissoryNoteAgreementsEntered_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Promissory Note Agreements Entered</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfPromissoryNoteAgreementsEntered_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of promissory note agreements entered</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfVehiclesAcquiredThroughLoans" xlink:label="cntm_NumberOfVehiclesAcquiredThroughLoans" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfVehiclesAcquiredThroughLoans" xlink:to="cntm_NumberOfVehiclesAcquiredThroughLoans_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfVehiclesAcquiredThroughLoans_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of vehicles acquired by the entity through issuance of vehicle loans as of the reporting date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfVehiclesAcquiredThroughLoans_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Vehicles Acquired Through Loans</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfVehiclesAcquiredThroughLoans_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of vehicles acquired</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfVehicleLoansDefault" xlink:label="cntm_NumberOfVehicleLoansDefault" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfVehicleLoansDefault" xlink:to="cntm_NumberOfVehicleLoansDefault_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfVehicleLoansDefault_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of vehicle loans defaulted.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfVehicleLoansDefault_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Vehicle Loans Default</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfVehicleLoansDefault_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of vehicle loans defaulted</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SaleOfFutureReceivableAgreementMember" xlink:label="cntm_SaleOfFutureReceivableAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SaleOfFutureReceivableAgreementMember" xlink:to="cntm_SaleOfFutureReceivableAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SaleOfFutureReceivableAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to sale of future receivable agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SaleOfFutureReceivableAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Future Receivable Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SaleOfFutureReceivableAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Future Receivable Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_RepaymentsOfNotesPayablePrincipalPortion" xlink:label="cntm_RepaymentsOfNotesPayablePrincipalPortion" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RepaymentsOfNotesPayablePrincipalPortion" xlink:to="cntm_RepaymentsOfNotesPayablePrincipalPortion_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RepaymentsOfNotesPayablePrincipalPortion_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash outflow relating to principal repayment of notes payable.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RepaymentsOfNotesPayablePrincipalPortion_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments Of Notes Payable, Principal Portion</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RepaymentsOfNotesPayablePrincipalPortion_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Principal amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_RepaymentsOfNotesPayableInterestPortion" xlink:label="cntm_RepaymentsOfNotesPayableInterestPortion" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RepaymentsOfNotesPayableInterestPortion" xlink:to="cntm_RepaymentsOfNotesPayableInterestPortion_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RepaymentsOfNotesPayableInterestPortion_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash outflow relating to payment of accrued interest on notes payable.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RepaymentsOfNotesPayableInterestPortion_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments Of Notes Payable, Interest Portion</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_RepaymentsOfNotesPayableInterestPortion_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repaid of accrued interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesPayableCurrent" xlink:label="us-gaap_NotesPayableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesPayableCurrent" xlink:to="us-gaap_NotesPayableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NotesPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NotesPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt, net of debt discount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebt" xlink:label="us-gaap_LongTermDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebt" xlink:to="us-gaap_LongTermDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_LongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount owed to lender</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_January2024SaleOfFutureReceiptsAgreementMember" xlink:label="cntm_January2024SaleOfFutureReceiptsAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_January2024SaleOfFutureReceiptsAgreementMember" xlink:to="cntm_January2024SaleOfFutureReceiptsAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_January2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to January 2024 sale of future receipts agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_January2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">January 2024 Sale Of Future Receipts Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_January2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">January 4, 2024</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AmendedJanuary2024SaleOfFutureReceiptsAgreementMember" xlink:label="cntm_AmendedJanuary2024SaleOfFutureReceiptsAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AmendedJanuary2024SaleOfFutureReceiptsAgreementMember" xlink:to="cntm_AmendedJanuary2024SaleOfFutureReceiptsAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AmendedJanuary2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to amended January 2024 sale of future receipts agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AmendedJanuary2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amended January 2024 Sale Of Future Receipts Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AmendedJanuary2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">January 30, 2024</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SecondJanuary2024SaleOfFutureReceiptsAgreementMember" xlink:label="cntm_SecondJanuary2024SaleOfFutureReceiptsAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SecondJanuary2024SaleOfFutureReceiptsAgreementMember" xlink:to="cntm_SecondJanuary2024SaleOfFutureReceiptsAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SecondJanuary2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to second January 2024 sale of future receipts agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SecondJanuary2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second January 2024 Sale Of Future Receipts Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SecondJanuary2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second January 30, 2024</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_May2024SaleOfFutureReceiptsAgreementMember" xlink:label="cntm_May2024SaleOfFutureReceiptsAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_May2024SaleOfFutureReceiptsAgreementMember" xlink:to="cntm_May2024SaleOfFutureReceiptsAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_May2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to May 2024 sale of future receipts agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_May2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">May 2024 Sale Of Future Receipts Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_May2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">May 23, 2024</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_October2024SaleOfFutureReceiptsAgreementMember" xlink:label="cntm_October2024SaleOfFutureReceiptsAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_October2024SaleOfFutureReceiptsAgreementMember" xlink:to="cntm_October2024SaleOfFutureReceiptsAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_October2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to October 2024 sale of future receipts agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_October2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">October 2024 Sale Of Future Receipts Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_October2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">October 2024</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SecondMay2024SaleOfFutureReceiptsAgreementMember" xlink:label="cntm_SecondMay2024SaleOfFutureReceiptsAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SecondMay2024SaleOfFutureReceiptsAgreementMember" xlink:to="cntm_SecondMay2024SaleOfFutureReceiptsAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SecondMay2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to second May 2024 sale of future receipts agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SecondMay2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second May 2024 Sale Of Future Receipts Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SecondMay2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second May 2024</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_November2024SaleOfFutureReceiptsAgreementMember" xlink:label="cntm_November2024SaleOfFutureReceiptsAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_November2024SaleOfFutureReceiptsAgreementMember" xlink:to="cntm_November2024SaleOfFutureReceiptsAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_November2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to November 2024 sale of future receipts agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_November2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">November 2024 Sale Of Future Receipts Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_November2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">November 2024</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_July2024SaleOfFutureReceiptsAgreementMember" xlink:label="cntm_July2024SaleOfFutureReceiptsAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_July2024SaleOfFutureReceiptsAgreementMember" xlink:to="cntm_July2024SaleOfFutureReceiptsAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_July2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to July 2024 sale of future receipts agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_July2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">July 2024 Sale Of Future Receipts Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_July2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">July 24, 2024</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SecondNovember2024SaleOfFutureReceiptsAgreementMember" xlink:label="cntm_SecondNovember2024SaleOfFutureReceiptsAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SecondNovember2024SaleOfFutureReceiptsAgreementMember" xlink:to="cntm_SecondNovember2024SaleOfFutureReceiptsAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SecondNovember2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to second November 2024 sale of future receipts agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SecondNovember2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second November 2024 Sale Of Future Receipts Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SecondNovember2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second November 2024</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_September2024SaleOfFutureReceiptsAgreementMember" xlink:label="cntm_September2024SaleOfFutureReceiptsAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_September2024SaleOfFutureReceiptsAgreementMember" xlink:to="cntm_September2024SaleOfFutureReceiptsAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_September2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to September 2024 sale of future receipts agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_September2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">September 2024 Sale Of Future Receipts Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_September2024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">September 19, 2024</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_November82024SaleOfFutureReceiptsAgreementMember" xlink:label="cntm_November82024SaleOfFutureReceiptsAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_November82024SaleOfFutureReceiptsAgreementMember" xlink:to="cntm_November82024SaleOfFutureReceiptsAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_November82024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to November 8, 2024 sale of future receipts agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_November82024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">November 8, 2024 Sale Of Future Receipts Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_November82024SaleOfFutureReceiptsAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">November 8, 2024</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_UnamortizedDebtDiscountRemittance" xlink:label="cntm_UnamortizedDebtDiscountRemittance" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_UnamortizedDebtDiscountRemittance" xlink:to="cntm_UnamortizedDebtDiscountRemittance_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_UnamortizedDebtDiscountRemittance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount, after accumulated amortization, of debt discount.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_UnamortizedDebtDiscountRemittance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unamortized debt discount remittance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_UnamortizedDebtDiscountRemittance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unamortized debt discount remittance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentPercentageOfSalesReceiptsToBeRemitted" xlink:label="cntm_DebtInstrumentPercentageOfSalesReceiptsToBeRemitted" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentPercentageOfSalesReceiptsToBeRemitted" xlink:to="cntm_DebtInstrumentPercentageOfSalesReceiptsToBeRemitted_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentPercentageOfSalesReceiptsToBeRemitted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of sales receipts to be remitted by the entity as per the terms of the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentPercentageOfSalesReceiptsToBeRemitted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Percentage Of Sales Receipts To Be Remitted</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentPercentageOfSalesReceiptsToBeRemitted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of sales receipts to be remitted</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProceedsFromAdditionalAdvanceInSaleOfFutureReceipts" xlink:label="cntm_ProceedsFromAdditionalAdvanceInSaleOfFutureReceipts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromAdditionalAdvanceInSaleOfFutureReceipts" xlink:to="cntm_ProceedsFromAdditionalAdvanceInSaleOfFutureReceipts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromAdditionalAdvanceInSaleOfFutureReceipts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The cash inflow from the additional advance from sale of future receipts by the entity for the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromAdditionalAdvanceInSaleOfFutureReceipts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Additional Advance In Sale Of Future Receipts</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsFromAdditionalAdvanceInSaleOfFutureReceipts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional advance from sale of future receipts</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LitigationSettlementAmountAwardedToOtherParty" xlink:label="us-gaap_LitigationSettlementAmountAwardedToOtherParty" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LitigationSettlementAmountAwardedToOtherParty" xlink:to="us-gaap_LitigationSettlementAmountAwardedToOtherParty_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LitigationSettlementAmountAwardedToOtherParty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Litigation Settlement, Amount Awarded to Other Party</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LitigationSettlementAmountAwardedToOtherParty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LitigationSettlementConditionalPaymentAmountHeldByThirdParty" xlink:label="cntm_LitigationSettlementConditionalPaymentAmountHeldByThirdParty" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LitigationSettlementConditionalPaymentAmountHeldByThirdParty" xlink:to="cntm_LitigationSettlementConditionalPaymentAmountHeldByThirdParty_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LitigationSettlementConditionalPaymentAmountHeldByThirdParty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of conditional payment required as per the terms of the litigation settlement from amount held by third party during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LitigationSettlementConditionalPaymentAmountHeldByThirdParty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Litigation Settlement, Conditional Payment Amount, Held By Third Party</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LitigationSettlementConditionalPaymentAmountHeldByThirdParty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of conditional payment by a third party</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForLegalSettlements" xlink:label="us-gaap_PaymentsForLegalSettlements" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsForLegalSettlements" xlink:to="us-gaap_PaymentsForLegalSettlements_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsForLegalSettlements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments for Legal Settlements</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsForLegalSettlements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Monthly payments required as per settlement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit Facility, Maximum Borrowing Capacity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum borrowing capacity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromLinesOfCredit" xlink:label="us-gaap_ProceedsFromLinesOfCredit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromLinesOfCredit" xlink:to="us-gaap_ProceedsFromLinesOfCredit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromLinesOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Lines of Credit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromLinesOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount borrowed</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentPeriodicPaymentNumberOfInstallments" xlink:label="cntm_DebtInstrumentPeriodicPaymentNumberOfInstallments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentPeriodicPaymentNumberOfInstallments" xlink:to="cntm_DebtInstrumentPeriodicPaymentNumberOfInstallments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentPeriodicPaymentNumberOfInstallments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of installments for payment of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentPeriodicPaymentNumberOfInstallments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Periodic Payment, Number Of Installments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentPeriodicPaymentNumberOfInstallments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Periodic payment, number of installments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FinancingFacilityRepaymentOfAdvanceBorrowed" xlink:label="cntm_FinancingFacilityRepaymentOfAdvanceBorrowed" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityRepaymentOfAdvanceBorrowed" xlink:to="cntm_FinancingFacilityRepaymentOfAdvanceBorrowed_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityRepaymentOfAdvanceBorrowed_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The cash outflow related to repayment of advance borrowed under financing facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityRepaymentOfAdvanceBorrowed_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Repayment Of Advance Borrowed</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityRepaymentOfAdvanceBorrowed_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayment of advance borrowed</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FinancingFacilityPaymentOfInterest" xlink:label="cntm_FinancingFacilityPaymentOfInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FinancingFacilityPaymentOfInterest" xlink:to="cntm_FinancingFacilityPaymentOfInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FinancingFacilityPaymentOfInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The cash outflow related to payment of interest under financing facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FinancingFacilityPaymentOfInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Facility, Payment Of Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FinancingFacilityPaymentOfInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment of interest</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_InsurancePremiumFinancingMember" xlink:label="cntm_InsurancePremiumFinancingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_InsurancePremiumFinancingMember" xlink:to="cntm_InsurancePremiumFinancingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_InsurancePremiumFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to insurance premium financing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_InsurancePremiumFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Insurance Premium Financing [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_InsurancePremiumFinancingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">D&amp;O Insurance Premium Financing</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedInsuranceCurrentAndNoncurrent" xlink:label="us-gaap_AccruedInsuranceCurrentAndNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccruedInsuranceCurrentAndNoncurrent" xlink:to="us-gaap_AccruedInsuranceCurrentAndNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccruedInsuranceCurrentAndNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued Insurance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccruedInsuranceCurrentAndNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued insurance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PaymentOfInsurancePremium" xlink:label="cntm_PaymentOfInsurancePremium" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentOfInsurancePremium" xlink:to="cntm_PaymentOfInsurancePremium_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentOfInsurancePremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of insurance premium paid during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentOfInsurancePremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment Of Insurance Premium</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_UmeshGoradiaMember" xlink:label="cntm_UmeshGoradiaMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_UmeshGoradiaMember" xlink:to="cntm_UmeshGoradiaMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_UmeshGoradiaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Umesh Goradia.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_UmeshGoradiaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Umesh Goradia [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_UmeshGoradiaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Umesh Goradia</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SaleOfFutureReceiptsTerminationPrincipalPayable" xlink:label="cntm_SaleOfFutureReceiptsTerminationPrincipalPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SaleOfFutureReceiptsTerminationPrincipalPayable" xlink:to="cntm_SaleOfFutureReceiptsTerminationPrincipalPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SaleOfFutureReceiptsTerminationPrincipalPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of remaining principal portion of debt payable due to termination of sale of future receipts agreements.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SaleOfFutureReceiptsTerminationPrincipalPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale Of Future Receipts, Termination, Principal Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SaleOfFutureReceiptsTerminationPrincipalPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining principal portion of debt payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentCollateralRedemptionOfShares" xlink:label="cntm_DebtInstrumentCollateralRedemptionOfShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentCollateralRedemptionOfShares" xlink:to="cntm_DebtInstrumentCollateralRedemptionOfShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentCollateralRedemptionOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of shares held by the lender as collateral which can be redeemed after full repayment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentCollateralRedemptionOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Collateral, Redemption Of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentCollateralRedemptionOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtBalanceReductionDueToSaleOfStock" xlink:label="cntm_DebtBalanceReductionDueToSaleOfStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtBalanceReductionDueToSaleOfStock" xlink:to="cntm_DebtBalanceReductionDueToSaleOfStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtBalanceReductionDueToSaleOfStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The reduction in debt balances resulting from the offset through stock issuances.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtBalanceReductionDueToSaleOfStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Balance Reduction, Due To Sale of Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtBalanceReductionDueToSaleOfStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reduction of debt balance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtModificationPresentValueDifferenceBetweenOriginalAndRevisedCashFlowsPercent" xlink:label="cntm_DebtModificationPresentValueDifferenceBetweenOriginalAndRevisedCashFlowsPercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtModificationPresentValueDifferenceBetweenOriginalAndRevisedCashFlowsPercent" xlink:to="cntm_DebtModificationPresentValueDifferenceBetweenOriginalAndRevisedCashFlowsPercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtModificationPresentValueDifferenceBetweenOriginalAndRevisedCashFlowsPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percent of present value difference between the original and revised cash flows for debt modification</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtModificationPresentValueDifferenceBetweenOriginalAndRevisedCashFlowsPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Modification, Present Value Difference Between Original and Revised Cash Flows, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtModificationPresentValueDifferenceBetweenOriginalAndRevisedCashFlowsPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt modification, difference between original and revised cash flow, percent</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:to="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Authorized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of awards authorized</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Options</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding at beginning</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding at ending</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Number</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vested and exercisable at ending</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted-average Exercise Price</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding at beginning</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding at ending</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted Average Exercise Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vested and exercisable at ending</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Additional Disclosures [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted-average Remaining Contractual Life</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:to="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding at ending</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1" xlink:to="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted Average Remaining Contractual Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vested and exercisable at ending</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestAbstract" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestAbstract" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate Intrinsic Value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Intrinsic Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding at ending</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1" xlink:to="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Intrinsic Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intrinsic value of exercisable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:to="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrecognized compensation cost</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameAxis" xlink:label="us-gaap_PlanNameAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PlanNameAxis" xlink:to="us-gaap_PlanNameAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PlanNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Plan Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameDomain" xlink:label="us-gaap_PlanNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PlanNameDomain" xlink:to="us-gaap_PlanNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PlanNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Plan Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EquityIncentivePlan2019Member" xlink:label="cntm_EquityIncentivePlan2019Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquityIncentivePlan2019Member" xlink:to="cntm_EquityIncentivePlan2019Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquityIncentivePlan2019Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to 2019 Equity Incentive Plan.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquityIncentivePlan2019Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Incentive Plan 2019 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_EquityIncentivePlan2019Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2019 Equity Incentive Plan</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EquityIncentivePlan2023Member" xlink:label="cntm_EquityIncentivePlan2023Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquityIncentivePlan2023Member" xlink:to="cntm_EquityIncentivePlan2023Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquityIncentivePlan2023Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Equity Incentive Plan 2023.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquityIncentivePlan2023Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Incentive Plan 2023 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EquityIncentivePlan2023Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2023 Equity Incentive Plan</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CapitalMarketsAdvisoryAgreementMember" xlink:label="cntm_CapitalMarketsAdvisoryAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CapitalMarketsAdvisoryAgreementMember" xlink:to="cntm_CapitalMarketsAdvisoryAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CapitalMarketsAdvisoryAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to capital markets advisory agreement (the "CMA Agreement").</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CapitalMarketsAdvisoryAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital Markets Advisory Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CapitalMarketsAdvisoryAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital Markets Advisory Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MarketingServicesAgreementMember" xlink:label="cntm_MarketingServicesAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MarketingServicesAgreementMember" xlink:to="cntm_MarketingServicesAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MarketingServicesAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to marketing services agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MarketingServicesAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Marketing Services Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MarketingServicesAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Marketing Services Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_M1ServicesAgreementWithServiceProviderOneMember" xlink:label="cntm_M1ServicesAgreementWithServiceProviderOneMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_M1ServicesAgreementWithServiceProviderOneMember" xlink:to="cntm_M1ServicesAgreementWithServiceProviderOneMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_M1ServicesAgreementWithServiceProviderOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to services agreement with service provider one.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_M1ServicesAgreementWithServiceProviderOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">M1 Services Agreement with Service Provider One [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_M1ServicesAgreementWithServiceProviderOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Service provider one</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_M2ServicesAgreementWithServiceProviderTwoMember" xlink:label="cntm_M2ServicesAgreementWithServiceProviderTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_M2ServicesAgreementWithServiceProviderTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to services agreement with service provider two.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_M2ServicesAgreementWithServiceProviderTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">M2 Services Agreement with Service Provider Two [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_M2ServicesAgreementWithServiceProviderTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Service provider two</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ServiceAgreementMember" xlink:label="cntm_ServiceAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ServiceAgreementMember" xlink:to="cntm_ServiceAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ServiceAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to service agreements.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ServiceAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Service Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ServiceAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Service Agreements</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockMember" xlink:label="us-gaap_RestrictedStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RestrictedStockMember" xlink:to="us-gaap_RestrictedStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RestrictedStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RestrictedStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted shares</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GranteeStatusAxis" xlink:label="us-gaap_GranteeStatusAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GranteeStatusAxis" xlink:to="us-gaap_GranteeStatusAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GranteeStatusAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Grantee Status [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GranteeStatusDomain" xlink:label="us-gaap_GranteeStatusDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GranteeStatusDomain" xlink:to="us-gaap_GranteeStatusDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GranteeStatusDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Grantee Status [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedPaymentArrangementEmployeeMember" xlink:label="us-gaap_ShareBasedPaymentArrangementEmployeeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedPaymentArrangementEmployeeMember" xlink:to="us-gaap_ShareBasedPaymentArrangementEmployeeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedPaymentArrangementEmployeeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Employee [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedPaymentArrangementEmployeeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Director and employee</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedPaymentArrangementNonemployeeMember" xlink:label="us-gaap_ShareBasedPaymentArrangementNonemployeeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedPaymentArrangementNonemployeeMember" xlink:to="us-gaap_ShareBasedPaymentArrangementNonemployeeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedPaymentArrangementNonemployeeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Nonemployee [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedPaymentArrangementNonemployeeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nonemployee</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Percentage of Outstanding Stock Maximum</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of maximum number of shares issued</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfIncreaseInOutstandingStock" xlink:label="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfIncreaseInOutstandingStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfIncreaseInOutstandingStock" xlink:to="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfIncreaseInOutstandingStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfIncreaseInOutstandingStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of additional shares that may be issued in accordance with the plan as a proportion of outstanding capital stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfIncreaseInOutstandingStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Percentage of Increase in Outstanding Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfIncreaseInOutstandingStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of increase in outstanding stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesGranted" xlink:label="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesGranted" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesGranted" xlink:to="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesGranted_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesGranted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares granted under share-based payment arrangement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesGranted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Shares Granted</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesGranted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares granted</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:to="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Expiration Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expiration Period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableCurrentAndNoncurrent" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsPayableCurrentAndNoncurrent" xlink:to="us-gaap_AccountsPayableCurrentAndNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfDaysVolumeWeightedAveragePriceForShareResetAdjustment" xlink:label="cntm_NumberOfDaysVolumeWeightedAveragePriceForShareResetAdjustment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfDaysVolumeWeightedAveragePriceForShareResetAdjustment" xlink:to="cntm_NumberOfDaysVolumeWeightedAveragePriceForShareResetAdjustment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfDaysVolumeWeightedAveragePriceForShareResetAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the number of days volume weighted average price considered for share reset adjustment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfDaysVolumeWeightedAveragePriceForShareResetAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Days Volume Weighted Average Price for Share Reset Adjustment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfDaysVolumeWeightedAveragePriceForShareResetAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of days for share reset adjustment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ShareResetTriggerPricePerShare" xlink:label="cntm_ShareResetTriggerPricePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ShareResetTriggerPricePerShare" xlink:to="cntm_ShareResetTriggerPricePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ShareResetTriggerPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the share reset trigger price per share.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ShareResetTriggerPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Reset Trigger Price Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ShareResetTriggerPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share price</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ShareAdjustmentFloorPricePerShare" xlink:label="cntm_ShareAdjustmentFloorPricePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ShareAdjustmentFloorPricePerShare" xlink:to="cntm_ShareAdjustmentFloorPricePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ShareAdjustmentFloorPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the share adjustment floor price per share.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ShareAdjustmentFloorPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Adjustment Floor Price Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ShareAdjustmentFloorPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Floor Price</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:to="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total unrecognized compensation expense related to unvested founder shares</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:to="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted average service period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfServiceProviders" xlink:label="cntm_NumberOfServiceProviders" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfServiceProviders" xlink:to="cntm_NumberOfServiceProviders_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfServiceProviders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the number of service providers.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfServiceProviders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Service Providers</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfServiceProviders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of service providers</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Requisite Service Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Service period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted shares of the company's common stock that are unvested</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantedInPeriodValue" xlink:label="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantedInPeriodValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantedInPeriodValue" xlink:to="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantedInPeriodValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantedInPeriodValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The value of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantedInPeriodValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Granted in Period, Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantedInPeriodValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of restricted stock granted during the period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeTable" xlink:label="us-gaap_DerivativeTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeTable" xlink:to="us-gaap_DerivativeTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative [Table]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ShareResetDerivativeLiabilityMember" xlink:label="cntm_ShareResetDerivativeLiabilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ShareResetDerivativeLiabilityMember" xlink:to="cntm_ShareResetDerivativeLiabilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ShareResetDerivativeLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to share reset derivative liability.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ShareResetDerivativeLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Reset Derivative Liability [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ShareResetDerivativeLiabilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Reset Derivative Liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLineItems" xlink:label="us-gaap_DerivativeLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeLineItems" xlink:to="us-gaap_DerivativeLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DERIVATIVE FINANCIAL INSTRUMENTS</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DerivativesNumberOfConversionAgreements" xlink:label="cntm_DerivativesNumberOfConversionAgreements" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DerivativesNumberOfConversionAgreements" xlink:to="cntm_DerivativesNumberOfConversionAgreements_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DerivativesNumberOfConversionAgreements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of conversion agreements under derivative contracts.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DerivativesNumberOfConversionAgreements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivatives, Number Of Conversion Agreements</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DerivativesNumberOfConversionAgreements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of conversion agreements</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DerivativesNumberOfConversionAgreementsWithRelatedParties" xlink:label="cntm_DerivativesNumberOfConversionAgreementsWithRelatedParties" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DerivativesNumberOfConversionAgreementsWithRelatedParties" xlink:to="cntm_DerivativesNumberOfConversionAgreementsWithRelatedParties_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DerivativesNumberOfConversionAgreementsWithRelatedParties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of conversion agreements with related parties under derivative contracts.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DerivativesNumberOfConversionAgreementsWithRelatedParties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivatives, Number Of Conversion Agreements With Related Parties</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DerivativesNumberOfConversionAgreementsWithRelatedParties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of conversion agreements with related parties</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ThresholdTradingDaysPriorToResetDateComputationOfVolumeWeightedAveragePrice" xlink:label="cntm_ThresholdTradingDaysPriorToResetDateComputationOfVolumeWeightedAveragePrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ThresholdTradingDaysPriorToResetDateComputationOfVolumeWeightedAveragePrice" xlink:to="cntm_ThresholdTradingDaysPriorToResetDateComputationOfVolumeWeightedAveragePrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ThresholdTradingDaysPriorToResetDateComputationOfVolumeWeightedAveragePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold trading days prior to reset date for computation of volume weighted average price.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ThresholdTradingDaysPriorToResetDateComputationOfVolumeWeightedAveragePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold Trading Days Prior To Reset Date, Computation Of Volume Weighted Average Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ThresholdTradingDaysPriorToResetDateComputationOfVolumeWeightedAveragePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold trading days prior to reset date</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MinimumResetPrice" xlink:label="cntm_MinimumResetPrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MinimumResetPrice" xlink:to="cntm_MinimumResetPrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MinimumResetPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Denotes minimum reset price.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MinimumResetPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum Reset Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MinimumResetPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum reset price</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ThresholdPeriodFromConversionAgreementDateComputationOfResetDate" xlink:label="cntm_ThresholdPeriodFromConversionAgreementDateComputationOfResetDate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ThresholdPeriodFromConversionAgreementDateComputationOfResetDate" xlink:to="cntm_ThresholdPeriodFromConversionAgreementDateComputationOfResetDate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ThresholdPeriodFromConversionAgreementDateComputationOfResetDate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold period for computation of reset date from the date of conversion agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ThresholdPeriodFromConversionAgreementDateComputationOfResetDate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold Period From Conversion Agreement Date, Computation Of Reset Date</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ThresholdPeriodFromConversionAgreementDateComputationOfResetDate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold period for computation of reset date from the date of conversion agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DerivativeConversionPrice" xlink:label="cntm_DerivativeConversionPrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DerivativeConversionPrice" xlink:to="cntm_DerivativeConversionPrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DerivativeConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The conversion price under derivative contract.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DerivativeConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Conversion Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DerivativeConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion price</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FpaTerminationAgreementMember" xlink:label="cntm_FpaTerminationAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FpaTerminationAgreementMember" xlink:to="cntm_FpaTerminationAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FpaTerminationAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to FPA Termination Agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FpaTerminationAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fpa Termination Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FpaTerminationAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">FPA Termination Agreement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeteoraSpecialOpportunityFundMember" xlink:label="cntm_MeteoraSpecialOpportunityFundMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeteoraSpecialOpportunityFundMember" xlink:to="cntm_MeteoraSpecialOpportunityFundMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeteoraSpecialOpportunityFundMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Meteora Special Opportunity Fund.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeteoraSpecialOpportunityFundMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Meteora Special Opportunity Fund [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeteoraSpecialOpportunityFundMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Meteora</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiarySaleOfStockAxis" xlink:label="us-gaap_SubsidiarySaleOfStockAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsidiarySaleOfStockAxis" xlink:to="us-gaap_SubsidiarySaleOfStockAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockNameOfTransactionDomain" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfSharesPurchasedFromRedeemingStockholders" xlink:label="cntm_NumberOfSharesPurchasedFromRedeemingStockholders" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfSharesPurchasedFromRedeemingStockholders" xlink:to="cntm_NumberOfSharesPurchasedFromRedeemingStockholders_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfSharesPurchasedFromRedeemingStockholders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares purchased from redeeming stockholders, pursuant to an arrangement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfSharesPurchasedFromRedeemingStockholders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Shares Purchased From Redeeming Stockholders</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfSharesPurchasedFromRedeemingStockholders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares purchased from redeeming stockholders</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CommonStockRedemptionPricePerShare" xlink:label="cntm_CommonStockRedemptionPricePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommonStockRedemptionPricePerShare" xlink:to="cntm_CommonStockRedemptionPricePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommonStockRedemptionPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The price per share at which the common stock of an entity is redeemed or may be called at.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommonStockRedemptionPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Redemption Price Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CommonStockRedemptionPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Price per share at which common stock redeemed</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PrepaymentsForPurchaseOfShares" xlink:label="cntm_PrepaymentsForPurchaseOfShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PrepaymentsForPurchaseOfShares" xlink:to="cntm_PrepaymentsForPurchaseOfShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PrepaymentsForPurchaseOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of prepayments made for the purchase of shares.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PrepaymentsForPurchaseOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepayments For Purchase Of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PrepaymentsForPurchaseOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepayment amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PercentageOfProductOfNumberOfRecycledSharesAndInitialPrice" xlink:label="cntm_PercentageOfProductOfNumberOfRecycledSharesAndInitialPrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PercentageOfProductOfNumberOfRecycledSharesAndInitialPrice" xlink:to="cntm_PercentageOfProductOfNumberOfRecycledSharesAndInitialPrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PercentageOfProductOfNumberOfRecycledSharesAndInitialPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of the product of number of recycled shares and the initial price.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PercentageOfProductOfNumberOfRecycledSharesAndInitialPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of the Product of Number of Recycled Shares and the Initial Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PercentageOfProductOfNumberOfRecycledSharesAndInitialPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of prepayment shortfall</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PercentageOfPaymentDueOutOfPrepaymentShortfall" xlink:label="cntm_PercentageOfPaymentDueOutOfPrepaymentShortfall" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PercentageOfPaymentDueOutOfPrepaymentShortfall" xlink:to="cntm_PercentageOfPaymentDueOutOfPrepaymentShortfall_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PercentageOfPaymentDueOutOfPrepaymentShortfall_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of payment due out of prepayment shortfall.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PercentageOfPaymentDueOutOfPrepaymentShortfall_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage Of Payment Due Out Of Prepayment Shortfall</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PercentageOfPaymentDueOutOfPrepaymentShortfall_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of payment due out of prepayment shortfall</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ReceivablesOfPrepaymentShortfallPayments" xlink:label="cntm_ReceivablesOfPrepaymentShortfallPayments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ReceivablesOfPrepaymentShortfallPayments" xlink:to="cntm_ReceivablesOfPrepaymentShortfallPayments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ReceivablesOfPrepaymentShortfallPayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of receivables of the payment made pursuant to prepayment shortfall.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ReceivablesOfPrepaymentShortfallPayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Receivables Of Prepayment Shortfall Payments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ReceivablesOfPrepaymentShortfallPayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Receivables of prepayment shortfall</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConsiderationEqualToProductAmount" xlink:label="cntm_ConsiderationEqualToProductAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConsiderationEqualToProductAmount" xlink:to="cntm_ConsiderationEqualToProductAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConsiderationEqualToProductAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of consideration equal to the product.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConsiderationEqualToProductAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration Equal To Product Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConsiderationEqualToProductAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration equal to product amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AdditionalConsiderationPaidForAdditionalSharesPurchased" xlink:label="cntm_AdditionalConsiderationPaidForAdditionalSharesPurchased" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AdditionalConsiderationPaidForAdditionalSharesPurchased" xlink:to="cntm_AdditionalConsiderationPaidForAdditionalSharesPurchased_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AdditionalConsiderationPaidForAdditionalSharesPurchased_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of additional consideration paid by the company, for the purpose of repayment for purchased additional shares from third parties prior to the Closing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AdditionalConsiderationPaidForAdditionalSharesPurchased_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Consideration Paid For Additional Shares Purchased</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AdditionalConsiderationPaidForAdditionalSharesPurchased_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of additional consideration</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PercentageOverProductOfPrepaymentAmount" xlink:label="cntm_PercentageOverProductOfPrepaymentAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PercentageOverProductOfPrepaymentAmount" xlink:to="cntm_PercentageOverProductOfPrepaymentAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PercentageOverProductOfPrepaymentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage over product of prepayment amount.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PercentageOverProductOfPrepaymentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage Over Product Of Prepayment Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PercentageOverProductOfPrepaymentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage over product of prepayment amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PaymentsOfOriginalAndAdditionalProductOfPrepaymentAmount" xlink:label="cntm_PaymentsOfOriginalAndAdditionalProductOfPrepaymentAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PaymentsOfOriginalAndAdditionalProductOfPrepaymentAmount" xlink:to="cntm_PaymentsOfOriginalAndAdditionalProductOfPrepaymentAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PaymentsOfOriginalAndAdditionalProductOfPrepaymentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of product of prepayment amount and additional product of prepayment amount.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PaymentsOfOriginalAndAdditionalProductOfPrepaymentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments Of Original And Additional Product Of Prepayment Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PaymentsOfOriginalAndAdditionalProductOfPrepaymentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of original and additional product of prepayment amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForBrokerageFees" xlink:label="us-gaap_PaymentsForBrokerageFees" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsForBrokerageFees" xlink:to="us-gaap_PaymentsForBrokerageFees_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsForBrokerageFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments for Brokerage Fees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsForBrokerageFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Brokerage expenses</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ReductionInPrepaymentShortfallPercentage" xlink:label="cntm_ReductionInPrepaymentShortfallPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ReductionInPrepaymentShortfallPercentage" xlink:to="cntm_ReductionInPrepaymentShortfallPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ReductionInPrepaymentShortfallPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of reduction in prepayment shortfall.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ReductionInPrepaymentShortfallPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reduction In Prepayment Shortfall, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ReductionInPrepaymentShortfallPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of reduction in prepayment shortfall</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AdditionalPrepaymentShortfallRequestValue" xlink:label="cntm_AdditionalPrepaymentShortfallRequestValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AdditionalPrepaymentShortfallRequestValue" xlink:to="cntm_AdditionalPrepaymentShortfallRequestValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AdditionalPrepaymentShortfallRequestValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional prepayment shortfall request interval amount.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AdditionalPrepaymentShortfallRequestValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Prepayment Shortfall Request, Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AdditionalPrepaymentShortfallRequestValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of additional shortfall request</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_RecoveryOfOutstandingPrepaymentShortfallPercentage" xlink:label="cntm_RecoveryOfOutstandingPrepaymentShortfallPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RecoveryOfOutstandingPrepaymentShortfallPercentage" xlink:to="cntm_RecoveryOfOutstandingPrepaymentShortfallPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RecoveryOfOutstandingPrepaymentShortfallPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recovery of an outstanding prepayment shortfall expressed as a percentage.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RecoveryOfOutstandingPrepaymentShortfallPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recovery Of Outstanding Prepayment Shortfall, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RecoveryOfOutstandingPrepaymentShortfallPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recovery of an outstanding prepayment shortfall (as percentage)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ReceivablesOfPrepaymentShortfallPaymentsWriteoff" xlink:label="cntm_ReceivablesOfPrepaymentShortfallPaymentsWriteoff" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ReceivablesOfPrepaymentShortfallPaymentsWriteoff" xlink:to="cntm_ReceivablesOfPrepaymentShortfallPaymentsWriteoff_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ReceivablesOfPrepaymentShortfallPaymentsWriteoff_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of receivables of the payment made writeoff pursuant to prepayment shortfall.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ReceivablesOfPrepaymentShortfallPaymentsWriteoff_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Receivables Of Prepayment Shortfall Payments Writeoff</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ReceivablesOfPrepaymentShortfallPaymentsWriteoff_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Receivables wrote off</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MinimumVolumeWeightedAveragePriceOfShares" xlink:label="cntm_MinimumVolumeWeightedAveragePriceOfShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MinimumVolumeWeightedAveragePriceOfShares" xlink:to="cntm_MinimumVolumeWeightedAveragePriceOfShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MinimumVolumeWeightedAveragePriceOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum VWAP Price of the Shares of the prior week.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MinimumVolumeWeightedAveragePriceOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum Volume Weighted Average Price of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MinimumVolumeWeightedAveragePriceOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum volume-weighted average price per share</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfSharesIssuedUnderForwardPurchaseAgreement" xlink:label="cntm_NumberOfSharesIssuedUnderForwardPurchaseAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfSharesIssuedUnderForwardPurchaseAgreement" xlink:to="cntm_NumberOfSharesIssuedUnderForwardPurchaseAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfSharesIssuedUnderForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued under forward purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfSharesIssuedUnderForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Shares Issued Under Forward Purchase Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfSharesIssuedUnderForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares sold pursuant</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInEarnings" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInEarnings" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInEarnings" xlink:to="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInEarnings_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInEarnings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Inputs Reconciliation, Gain (Loss) Included in Earnings</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInEarnings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on forward purchase assets</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SharesReleasedFromDesignationOfRecycledShares" xlink:label="cntm_SharesReleasedFromDesignationOfRecycledShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SharesReleasedFromDesignationOfRecycledShares" xlink:to="cntm_SharesReleasedFromDesignationOfRecycledShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SharesReleasedFromDesignationOfRecycledShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares released from designation as recycled shares.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SharesReleasedFromDesignationOfRecycledShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares Released From Designation Of Recycled Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SharesReleasedFromDesignationOfRecycledShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares released from designation as recycled shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MaximumCalendarDaysToProvideWrittenNoticeToRequestAdditionalPrepaymentShortfall" xlink:label="cntm_MaximumCalendarDaysToProvideWrittenNoticeToRequestAdditionalPrepaymentShortfall" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MaximumCalendarDaysToProvideWrittenNoticeToRequestAdditionalPrepaymentShortfall" xlink:to="cntm_MaximumCalendarDaysToProvideWrittenNoticeToRequestAdditionalPrepaymentShortfall_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MaximumCalendarDaysToProvideWrittenNoticeToRequestAdditionalPrepaymentShortfall_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum number of calendar days within which written notice is to be provided by the counterparty to the company, to request additional prepayment shortfall.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MaximumCalendarDaysToProvideWrittenNoticeToRequestAdditionalPrepaymentShortfall_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum Calendar Days To Provide Written Notice To Request Additional Prepayment Shortfall</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MaximumCalendarDaysToProvideWrittenNoticeToRequestAdditionalPrepaymentShortfall_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum number of days to provide written notice to request additional prepayment shortfall</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AdditionalShortfallRequestThresholdTradingDaysConsideredForVolumeWeightedAveragePrice" xlink:label="cntm_AdditionalShortfallRequestThresholdTradingDaysConsideredForVolumeWeightedAveragePrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AdditionalShortfallRequestThresholdTradingDaysConsideredForVolumeWeightedAveragePrice" xlink:to="cntm_AdditionalShortfallRequestThresholdTradingDaysConsideredForVolumeWeightedAveragePrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AdditionalShortfallRequestThresholdTradingDaysConsideredForVolumeWeightedAveragePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold trading days over which VWAP is considered for making a additional shortfall request.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AdditionalShortfallRequestThresholdTradingDaysConsideredForVolumeWeightedAveragePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Shortfall Request, Threshold Trading Days Considered For Volume Weighted Average Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AdditionalShortfallRequestThresholdTradingDaysConsideredForVolumeWeightedAveragePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of trading days prior to as additional shortfall request</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AdditionalShortfallRequestThresholdNumberOfTimesByWhichValueOfCurrentSharesLessShortfallSaleSharesShallBeGreaterThanAdditionalShortfallRequest" xlink:label="cntm_AdditionalShortfallRequestThresholdNumberOfTimesByWhichValueOfCurrentSharesLessShortfallSaleSharesShallBeGreaterThanAdditionalShortfallRequest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AdditionalShortfallRequestThresholdNumberOfTimesByWhichValueOfCurrentSharesLessShortfallSaleSharesShallBeGreaterThanAdditionalShortfallRequest" xlink:to="cntm_AdditionalShortfallRequestThresholdNumberOfTimesByWhichValueOfCurrentSharesLessShortfallSaleSharesShallBeGreaterThanAdditionalShortfallRequest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AdditionalShortfallRequestThresholdNumberOfTimesByWhichValueOfCurrentSharesLessShortfallSaleSharesShallBeGreaterThanAdditionalShortfallRequest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold number of times the value of current shares calculated by applying the VWAP price, less shortfall sale shares shall be greater than additional shortfall request, considered for making a additional shortfall request.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AdditionalShortfallRequestThresholdNumberOfTimesByWhichValueOfCurrentSharesLessShortfallSaleSharesShallBeGreaterThanAdditionalShortfallRequest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Shortfall Request, Threshold Number Of Times By Which Value Of Current Shares Less Shortfall Sale Shares Shall Be Greater Than Additional Shortfall Request</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AdditionalShortfallRequestThresholdNumberOfTimesByWhichValueOfCurrentSharesLessShortfallSaleSharesShallBeGreaterThanAdditionalShortfallRequest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of times the value of current shares is greater than additional shortfall request</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AdditionalShortfallRequestThresholdTradingDaysForAverageDailyValue" xlink:label="cntm_AdditionalShortfallRequestThresholdTradingDaysForAverageDailyValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AdditionalShortfallRequestThresholdTradingDaysForAverageDailyValue" xlink:to="cntm_AdditionalShortfallRequestThresholdTradingDaysForAverageDailyValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AdditionalShortfallRequestThresholdTradingDaysForAverageDailyValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold trading days over which average daily value is considered for making a additional shortfall request.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AdditionalShortfallRequestThresholdTradingDaysForAverageDailyValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Shortfall Request, Threshold Trading Days For Average Daily Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AdditionalShortfallRequestThresholdTradingDaysForAverageDailyValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of trading days prior to the average daily value in additional shortfall request</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AdditionalShortfallRequestThresholdNumberOfTimesByWhichAverageDailyValueTradedShallBeGreaterThanAdditionalShortfallRequest" xlink:label="cntm_AdditionalShortfallRequestThresholdNumberOfTimesByWhichAverageDailyValueTradedShallBeGreaterThanAdditionalShortfallRequest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AdditionalShortfallRequestThresholdNumberOfTimesByWhichAverageDailyValueTradedShallBeGreaterThanAdditionalShortfallRequest" xlink:to="cntm_AdditionalShortfallRequestThresholdNumberOfTimesByWhichAverageDailyValueTradedShallBeGreaterThanAdditionalShortfallRequest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AdditionalShortfallRequestThresholdNumberOfTimesByWhichAverageDailyValueTradedShallBeGreaterThanAdditionalShortfallRequest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold number of times the average daily value traded shall be greater than additional shortfall request, considered for making a additional shortfall request.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AdditionalShortfallRequestThresholdNumberOfTimesByWhichAverageDailyValueTradedShallBeGreaterThanAdditionalShortfallRequest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Shortfall Request, Threshold Number Of Times By Which Average Daily Value Traded Shall Be Greater Than Additional Shortfall Request</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AdditionalShortfallRequestThresholdNumberOfTimesByWhichAverageDailyValueTradedShallBeGreaterThanAdditionalShortfallRequest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of times the average daily value of shares is greater than additional shortfall request</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromDerivativeInstrumentFinancingActivities" xlink:label="us-gaap_ProceedsFromDerivativeInstrumentFinancingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromDerivativeInstrumentFinancingActivities" xlink:to="us-gaap_ProceedsFromDerivativeInstrumentFinancingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromDerivativeInstrumentFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Derivative Instrument, Financing Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromDerivativeInstrumentFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash proceeds</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ProceedsFromTerminationOfContract" xlink:label="cntm_ProceedsFromTerminationOfContract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ProceedsFromTerminationOfContract" xlink:to="cntm_ProceedsFromTerminationOfContract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ProceedsFromTerminationOfContract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amounts represents proceeds from termination of contract.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ProceedsFromTerminationOfContract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From termination Of Contract</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ProceedsFromTerminationOfContract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from termination of contract</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SharesDeemedFreeFromContractObligation" xlink:label="cntm_SharesDeemedFreeFromContractObligation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SharesDeemedFreeFromContractObligation" xlink:to="cntm_SharesDeemedFreeFromContractObligation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SharesDeemedFreeFromContractObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares free from contract obligation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SharesDeemedFreeFromContractObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares Deemed Free From Contract Obligation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_SharesDeemedFreeFromContractObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares deemed free and clear of all obligations</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfRecycledSharesOutstanding" xlink:label="cntm_NumberOfRecycledSharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfRecycledSharesOutstanding" xlink:to="cntm_NumberOfRecycledSharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfRecycledSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of recycled shares outstanding.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfRecycledSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Recycled Shares Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfRecycledSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of recycled shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DeemedAmountOfPrepaymentShortfall" xlink:label="cntm_DeemedAmountOfPrepaymentShortfall" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DeemedAmountOfPrepaymentShortfall" xlink:to="cntm_DeemedAmountOfPrepaymentShortfall_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DeemedAmountOfPrepaymentShortfall_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of prepayment shortfall receivable.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DeemedAmountOfPrepaymentShortfall_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deemed Amount Of Prepayment Shortfall</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DeemedAmountOfPrepaymentShortfall_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deemed amount of prepayment shortfall</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnExtinguishmentOfDebtAndVendorPayable" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnExtinguishmentOfDebtAndVendorPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnExtinguishmentOfDebtAndVendorPayable" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnExtinguishmentOfDebtAndVendorPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain (loss) on extinguishment of debt and vendor payable of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Gain (Loss) On Extinguishment Of Debt And Vendor Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnExtinguishmentOfDebtAndVendorPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on extinguishment of debt and vendor payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsReclassFromLevel3" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsReclassFromLevel3" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsReclassFromLevel3" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsReclassFromLevel3_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsReclassFromLevel3_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain (loss) recognized pertaining to change in fair value in income from asset measured at fair value on recurring basis using unobservable input (level 3).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsReclassFromLevel3_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Earnings, Reclass from level 3</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsReclassFromLevel3_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclass from level 3</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsChangeInFairValue" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsChangeInFairValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsChangeInFairValue" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsChangeInFairValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsChangeInFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain (loss) recognized pertaining to change in fair value in income from asset measured at fair value on recurring basis using unobservable input (level 3).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsChangeInFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Earnings, Change In Fair Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsChangeInFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputRemainingTermMember" xlink:label="cntm_MeasurementInputRemainingTermMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputRemainingTermMember" xlink:to="cntm_MeasurementInputRemainingTermMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputRemainingTermMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using remaining term.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputRemainingTermMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Remaining Term [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputRemainingTermMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining term</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputConversionPriceForPaymentsToBeMadeThroughIssuanceOfCommonStockMember" xlink:label="cntm_MeasurementInputConversionPriceForPaymentsToBeMadeThroughIssuanceOfCommonStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputConversionPriceForPaymentsToBeMadeThroughIssuanceOfCommonStockMember" xlink:to="cntm_MeasurementInputConversionPriceForPaymentsToBeMadeThroughIssuanceOfCommonStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputConversionPriceForPaymentsToBeMadeThroughIssuanceOfCommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using conversion price for payments to be made through issuance of common stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputConversionPriceForPaymentsToBeMadeThroughIssuanceOfCommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Conversion Price For Payments To Be Made Through Issuance Of Common Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputConversionPriceForPaymentsToBeMadeThroughIssuanceOfCommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion price for payments to be made through issuance of Company's common stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputPaymentsToBeMadeThroughIssuanceOfSharesOfCommonStockMember" xlink:label="cntm_MeasurementInputPaymentsToBeMadeThroughIssuanceOfSharesOfCommonStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputPaymentsToBeMadeThroughIssuanceOfSharesOfCommonStockMember" xlink:to="cntm_MeasurementInputPaymentsToBeMadeThroughIssuanceOfSharesOfCommonStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputPaymentsToBeMadeThroughIssuanceOfSharesOfCommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using payments to be made through issuance of shares of common stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputPaymentsToBeMadeThroughIssuanceOfSharesOfCommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Payments To Be Made Through Issuance Of Shares Of Common Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputPaymentsToBeMadeThroughIssuanceOfSharesOfCommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to be made through issuance of shares of Company's common stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputPaymentsToBeMadeInCashMember" xlink:label="cntm_MeasurementInputPaymentsToBeMadeInCashMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputPaymentsToBeMadeInCashMember" xlink:to="cntm_MeasurementInputPaymentsToBeMadeInCashMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputPaymentsToBeMadeInCashMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using payments to be made in cash.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputPaymentsToBeMadeInCashMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Payments To Be Made In Cash [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputPaymentsToBeMadeInCashMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to be made in cash</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputProbabilityOfMaturitySettlementScenarioMember" xlink:label="cntm_MeasurementInputProbabilityOfMaturitySettlementScenarioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputProbabilityOfMaturitySettlementScenarioMember" xlink:to="cntm_MeasurementInputProbabilityOfMaturitySettlementScenarioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputProbabilityOfMaturitySettlementScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using probability of maturity settlement scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputProbabilityOfMaturitySettlementScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Probability Of Maturity Settlement Scenario [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputProbabilityOfMaturitySettlementScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Probability of maturity settlement scenario</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputProbabilityOfPrepaymentShortfallSettlementScenarioMember" xlink:label="cntm_MeasurementInputProbabilityOfPrepaymentShortfallSettlementScenarioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputProbabilityOfPrepaymentShortfallSettlementScenarioMember" xlink:to="cntm_MeasurementInputProbabilityOfPrepaymentShortfallSettlementScenarioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputProbabilityOfPrepaymentShortfallSettlementScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using probability of prepayment shortfall settlement scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputProbabilityOfPrepaymentShortfallSettlementScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Probability Of Prepayment Shortfall Settlement Scenario [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputProbabilityOfPrepaymentShortfallSettlementScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Probability of prepayment shortfall settlement scenario</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputRecycledSharesHeldByMeteoraMember" xlink:label="cntm_MeasurementInputRecycledSharesHeldByMeteoraMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputRecycledSharesHeldByMeteoraMember" xlink:to="cntm_MeasurementInputRecycledSharesHeldByMeteoraMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputRecycledSharesHeldByMeteoraMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using recycled Shares held by Meteora.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputRecycledSharesHeldByMeteoraMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Recycled Shares Held By Meteora [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputRecycledSharesHeldByMeteoraMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recycled Shares held by Meteora</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputForecastedPricePerShareOfCommonStockAtMaturityMember" xlink:label="cntm_MeasurementInputForecastedPricePerShareOfCommonStockAtMaturityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputForecastedPricePerShareOfCommonStockAtMaturityMember" xlink:to="cntm_MeasurementInputForecastedPricePerShareOfCommonStockAtMaturityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputForecastedPricePerShareOfCommonStockAtMaturityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using forecasted price per share of common stock at maturity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputForecastedPricePerShareOfCommonStockAtMaturityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Forecasted Price Per Share Of Common Stock At Maturity [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputForecastedPricePerShareOfCommonStockAtMaturityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Forecasted price per share of Company's common stock at maturity</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputExpectedMarginFromMeteoraSSaleOfRecycledSharesMember" xlink:label="cntm_MeasurementInputExpectedMarginFromMeteoraSSaleOfRecycledSharesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputExpectedMarginFromMeteoraSSaleOfRecycledSharesMember" xlink:to="cntm_MeasurementInputExpectedMarginFromMeteoraSSaleOfRecycledSharesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputExpectedMarginFromMeteoraSSaleOfRecycledSharesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using expected margin from Meteora's sale of Recycled Shares.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputExpectedMarginFromMeteoraSSaleOfRecycledSharesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Expected Margin From Meteora'S Sale Of Recycled Shares [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputExpectedMarginFromMeteoraSSaleOfRecycledSharesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expected margin from Meteora's sale of Recycled Shares</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputExercisePriceMember" xlink:label="us-gaap_MeasurementInputExercisePriceMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MeasurementInputExercisePriceMember" xlink:to="us-gaap_MeasurementInputExercisePriceMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MeasurementInputExercisePriceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Exercise Price [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MeasurementInputExercisePriceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Exercise price</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputExpectedDividendRateMember" xlink:label="us-gaap_MeasurementInputExpectedDividendRateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MeasurementInputExpectedDividendRateMember" xlink:to="us-gaap_MeasurementInputExpectedDividendRateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MeasurementInputExpectedDividendRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Expected Dividend Rate [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MeasurementInputExpectedDividendRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividend rate</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputProbabilityOfCompletingBusinessCombinationMember" xlink:label="cntm_MeasurementInputProbabilityOfCompletingBusinessCombinationMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputProbabilityOfCompletingBusinessCombinationMember" xlink:to="cntm_MeasurementInputProbabilityOfCompletingBusinessCombinationMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputProbabilityOfCompletingBusinessCombinationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using probability of completing a Business Combination.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputProbabilityOfCompletingBusinessCombinationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Probability of completing a Business Combination</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputProbabilityOfCompletingBusinessCombinationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Probability of completing the Business Combination</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_Amended2024ForwardPurchaseAgreementMember" xlink:label="cntm_Amended2024ForwardPurchaseAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_Amended2024ForwardPurchaseAgreementMember" xlink:to="cntm_Amended2024ForwardPurchaseAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_Amended2024ForwardPurchaseAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Amended 2024 forward purchase agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_Amended2024ForwardPurchaseAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amended 2024 Forward Purchase Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_Amended2024ForwardPurchaseAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amended 2024 forward purchase agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetMeasurementInput" xlink:label="us-gaap_DerivativeAssetMeasurementInput" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeAssetMeasurementInput" xlink:to="us-gaap_DerivativeAssetMeasurementInput_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeAssetMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Asset, Measurement Input</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeAssetMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_UnrealizedGainLossOnDerivativesAssetsForwardPurchaseAgreementNet" xlink:label="cntm_UnrealizedGainLossOnDerivativesAssetsForwardPurchaseAgreementNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_UnrealizedGainLossOnDerivativesAssetsForwardPurchaseAgreementNet" xlink:to="cntm_UnrealizedGainLossOnDerivativesAssetsForwardPurchaseAgreementNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_UnrealizedGainLossOnDerivativesAssetsForwardPurchaseAgreementNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The total net change in the difference between the fair value and the carrying value, or in the comparative fair values, of forward purchase agreement derivative assets, held at each balance sheet date, that was included in earnings for the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_UnrealizedGainLossOnDerivativesAssetsForwardPurchaseAgreementNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrealized Gain Loss On Derivatives Assets Forward Purchase Agreement, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_UnrealizedGainLossOnDerivativesAssetsForwardPurchaseAgreementNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrealized gain (loss) on derivatives assets forward purchase agreement, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfDerivatives" xlink:label="us-gaap_GainLossOnSaleOfDerivatives" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnSaleOfDerivatives" xlink:to="us-gaap_GainLossOnSaleOfDerivatives_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainLossOnSaleOfDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Sale of Derivatives</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GainLossOnSaleOfDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on forward purchase agreement modification</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfSettlementOptions" xlink:label="cntm_NumberOfSettlementOptions" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfSettlementOptions" xlink:to="cntm_NumberOfSettlementOptions_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfSettlementOptions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the number of settlement options.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfSettlementOptions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Settlement Options</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfSettlementOptions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of settlement options</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DerivativeAssetThresholdTradingPriceForMaturitySettlement" xlink:label="cntm_DerivativeAssetThresholdTradingPriceForMaturitySettlement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DerivativeAssetThresholdTradingPriceForMaturitySettlement" xlink:to="cntm_DerivativeAssetThresholdTradingPriceForMaturitySettlement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DerivativeAssetThresholdTradingPriceForMaturitySettlement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the threshold trading price for the maturity settlements.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DerivativeAssetThresholdTradingPriceForMaturitySettlement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Asset, Threshold Trading price For Maturity Settlement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DerivativeAssetThresholdTradingPriceForMaturitySettlement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold trading price for maturity settlement</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_StockPriceDropsBelow1.09Member" xlink:label="cntm_StockPriceDropsBelow1.09Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_StockPriceDropsBelow1.09Member" xlink:to="cntm_StockPriceDropsBelow1.09Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_StockPriceDropsBelow1.09Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to the scenario when the stock price drops below $1.09.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_StockPriceDropsBelow1.09Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Price Drops Below $1.09 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_StockPriceDropsBelow1.09Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Price Drops Below $1.09</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_IfDefaultEventOccursMember" xlink:label="cntm_IfDefaultEventOccursMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_IfDefaultEventOccursMember" xlink:to="cntm_IfDefaultEventOccursMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_IfDefaultEventOccursMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to the scenario if default events occur.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_IfDefaultEventOccursMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">If Default Event Occurs [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_IfDefaultEventOccursMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">If Default Event Occurs</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SettlementAgreementThresholdDaysOfLowestVolumeWeightedAveragePriceConsidered" xlink:label="cntm_SettlementAgreementThresholdDaysOfLowestVolumeWeightedAveragePriceConsidered" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementAgreementThresholdDaysOfLowestVolumeWeightedAveragePriceConsidered" xlink:to="cntm_SettlementAgreementThresholdDaysOfLowestVolumeWeightedAveragePriceConsidered_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAgreementThresholdDaysOfLowestVolumeWeightedAveragePriceConsidered_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold days considered for volume weighted average price considered in arriving the number of shares issuable for other payables under settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementAgreementThresholdDaysOfLowestVolumeWeightedAveragePriceConsidered_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Agreement, Threshold Days Of Lowest Volume Weighted Average Price Considered</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAgreementThresholdDaysOfLowestVolumeWeightedAveragePriceConsidered_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Valuation period</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SettlementAgreementMinimumFloorPrice" xlink:label="cntm_SettlementAgreementMinimumFloorPrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementAgreementMinimumFloorPrice" xlink:to="cntm_SettlementAgreementMinimumFloorPrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAgreementMinimumFloorPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the minimum floor price i.e., purchase price used in issuing shares for other payables under settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementAgreementMinimumFloorPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Agreement, Minimum Floor Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAgreementMinimumFloorPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Floor price</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BeneficialOwnershipLimitPercentage" xlink:label="cntm_BeneficialOwnershipLimitPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BeneficialOwnershipLimitPercentage" xlink:to="cntm_BeneficialOwnershipLimitPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BeneficialOwnershipLimitPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum percentage of the Company's common stock that institutional investor can own.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BeneficialOwnershipLimitPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beneficial Ownership Limit, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BeneficialOwnershipLimitPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beneficial ownership (in percentage)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SettlementAgreementMaximumNumberOfSharesIssuable" xlink:label="cntm_SettlementAgreementMaximumNumberOfSharesIssuable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementAgreementMaximumNumberOfSharesIssuable" xlink:to="cntm_SettlementAgreementMaximumNumberOfSharesIssuable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAgreementMaximumNumberOfSharesIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum number of shares issuable under the settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementAgreementMaximumNumberOfSharesIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Agreement, Maximum Number Of Shares Issuable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAgreementMaximumNumberOfSharesIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum number of shares issuable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SettlementAgreementRemainingClaim" xlink:label="cntm_SettlementAgreementRemainingClaim" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementAgreementRemainingClaim" xlink:to="cntm_SettlementAgreementRemainingClaim_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAgreementRemainingClaim_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of remaining claim amount under settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementAgreementRemainingClaim_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Agreement, Remaining Claim</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAgreementRemainingClaim_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclaiming claim amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GainLossOnExtinguishmentOfOtherLiabilities" xlink:label="cntm_GainLossOnExtinguishmentOfOtherLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GainLossOnExtinguishmentOfOtherLiabilities" xlink:to="cntm_GainLossOnExtinguishmentOfOtherLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GainLossOnExtinguishmentOfOtherLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of gain (loss) upon extinguishment of other liabilities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GainLossOnExtinguishmentOfOtherLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) On Extinguishment Of Other Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GainLossOnExtinguishmentOfOtherLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on extinguishment of accounts payable</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SettlementAgreementRemainingClaimAmount" xlink:label="cntm_SettlementAgreementRemainingClaimAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SettlementAgreementRemainingClaimAmount" xlink:to="cntm_SettlementAgreementRemainingClaimAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SettlementAgreementRemainingClaimAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of remaining claim amount under settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SettlementAgreementRemainingClaimAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Agreement, Remaining Claim Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SettlementAgreementRemainingClaimAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining obligation</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EstimatedNumberOfSharesToBeIssued" xlink:label="cntm_EstimatedNumberOfSharesToBeIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EstimatedNumberOfSharesToBeIssued" xlink:to="cntm_EstimatedNumberOfSharesToBeIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EstimatedNumberOfSharesToBeIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to base case scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EstimatedNumberOfSharesToBeIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated Number Of Shares To Be Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EstimatedNumberOfSharesToBeIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share issued</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EstimatedFairValueOfSharesToBeIssued" xlink:label="cntm_EstimatedFairValueOfSharesToBeIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EstimatedFairValueOfSharesToBeIssued" xlink:to="cntm_EstimatedFairValueOfSharesToBeIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EstimatedFairValueOfSharesToBeIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The estimated fair value of the shares the company would issue to settle the remaining obligation at that date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EstimatedFairValueOfSharesToBeIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated Fair Value Of Shares To Be Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EstimatedFairValueOfSharesToBeIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate fair value</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DecreaseInStockPriceTrigger" xlink:label="cntm_DecreaseInStockPriceTrigger" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DecreaseInStockPriceTrigger" xlink:to="cntm_DecreaseInStockPriceTrigger_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DecreaseInStockPriceTrigger_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of per share decrease in stock price trigger.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DecreaseInStockPriceTrigger_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Decrease In Stock Price Trigger</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DecreaseInStockPriceTrigger_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Decrease in stock price trigger</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentConvertibleDecreaseInConversionPrice" xlink:label="cntm_DebtInstrumentConvertibleDecreaseInConversionPrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConvertibleDecreaseInConversionPrice" xlink:to="cntm_DebtInstrumentConvertibleDecreaseInConversionPrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConvertibleDecreaseInConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The decrease in price per share of the conversion feature embedded in the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConvertibleDecreaseInConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Decrease In Conversion Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConvertibleDecreaseInConversionPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion price</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfAdditionalSharesToBeIssuedToSatisfyRemainingClaim" xlink:label="cntm_NumberOfAdditionalSharesToBeIssuedToSatisfyRemainingClaim" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfAdditionalSharesToBeIssuedToSatisfyRemainingClaim" xlink:to="cntm_NumberOfAdditionalSharesToBeIssuedToSatisfyRemainingClaim_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfAdditionalSharesToBeIssuedToSatisfyRemainingClaim_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of additional shares to be issued to satisfy the remaining claim amount.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfAdditionalSharesToBeIssuedToSatisfyRemainingClaim_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Additional Shares To Be Issued To Satisfy Remaining Claim</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfAdditionalSharesToBeIssuedToSatisfyRemainingClaim_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional shares to be issued</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AmountOfInstallmentInRemainingTranche" xlink:label="cntm_AmountOfInstallmentInRemainingTranche" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AmountOfInstallmentInRemainingTranche" xlink:to="cntm_AmountOfInstallmentInRemainingTranche_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AmountOfInstallmentInRemainingTranche_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of installment in the remaining tranche of the settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AmountOfInstallmentInRemainingTranche_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount Of Installment In Remaining Tranche</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AmountOfInstallmentInRemainingTranche_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Installment in the remaining tranche</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_AmountOfInstallmentInFinalTranche" xlink:label="cntm_AmountOfInstallmentInFinalTranche" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_AmountOfInstallmentInFinalTranche" xlink:to="cntm_AmountOfInstallmentInFinalTranche_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_AmountOfInstallmentInFinalTranche_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of installment in the final tranche of the settlement agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_AmountOfInstallmentInFinalTranche_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount Of Installment In Final Tranche</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_AmountOfInstallmentInFinalTranche_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Installment in the final tranche</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputOperatingLeverageMember" xlink:label="cntm_MeasurementInputOperatingLeverageMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputOperatingLeverageMember" xlink:to="cntm_MeasurementInputOperatingLeverageMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputOperatingLeverageMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using operating leverage.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputOperatingLeverageMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Operating Leverage [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputOperatingLeverageMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating leverage</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputRevenueVolatilityMember" xlink:label="cntm_MeasurementInputRevenueVolatilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputRevenueVolatilityMember" xlink:to="cntm_MeasurementInputRevenueVolatilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputRevenueVolatilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using revenue volatility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputRevenueVolatilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Revenue Volatility [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputRevenueVolatilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue volatility</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputEbitdaVolatilityMember" xlink:label="cntm_MeasurementInputEbitdaVolatilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputEbitdaVolatilityMember" xlink:to="cntm_MeasurementInputEbitdaVolatilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputEbitdaVolatilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using EBITDA volatility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputEbitdaVolatilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Ebitda Volatility [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputEbitdaVolatilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">EBITDA volatility</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputEarnoutRiskFreeRateMember" xlink:label="cntm_MeasurementInputEarnoutRiskFreeRateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputEarnoutRiskFreeRateMember" xlink:to="cntm_MeasurementInputEarnoutRiskFreeRateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputEarnoutRiskFreeRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using earnout risk free rate.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputEarnoutRiskFreeRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Earnout Risk Free Rate [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputEarnoutRiskFreeRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnout risk free rate</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputLongTermRiskFreeRateMember" xlink:label="cntm_MeasurementInputLongTermRiskFreeRateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputLongTermRiskFreeRateMember" xlink:to="cntm_MeasurementInputLongTermRiskFreeRateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputLongTermRiskFreeRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using long-term risk-free rate.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputLongTermRiskFreeRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Long-Term Risk-Free Rate [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputLongTermRiskFreeRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term risk-free rate</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputWeightedAverageCostOfCapitalMember" xlink:label="cntm_MeasurementInputWeightedAverageCostOfCapitalMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputWeightedAverageCostOfCapitalMember" xlink:to="cntm_MeasurementInputWeightedAverageCostOfCapitalMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputWeightedAverageCostOfCapitalMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using weighted average cost of capital.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputWeightedAverageCostOfCapitalMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Weighted Average Cost Of Capital [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputWeightedAverageCostOfCapitalMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted average cost of capital</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputCorrelationBetweenRevenueAndEbitdaMember" xlink:label="cntm_MeasurementInputCorrelationBetweenRevenueAndEbitdaMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputCorrelationBetweenRevenueAndEbitdaMember" xlink:to="cntm_MeasurementInputCorrelationBetweenRevenueAndEbitdaMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputCorrelationBetweenRevenueAndEbitdaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using correlation between revenue and EBITDA.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputCorrelationBetweenRevenueAndEbitdaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Correlation Between Revenue And Ebitda [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputCorrelationBetweenRevenueAndEbitdaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Correlation between revenue and EBITDA</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputTermToPaymentMember" xlink:label="cntm_MeasurementInputTermToPaymentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputTermToPaymentMember" xlink:to="cntm_MeasurementInputTermToPaymentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputTermToPaymentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using term to payment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputTermToPaymentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Term To Payment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputTermToPaymentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term to payment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput" xlink:to="us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Liability, Measurement Input</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration obligation measurement input</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MeasurementInputForecastedFiveDayVwapPerShareOfCommonStockMember" xlink:label="cntm_MeasurementInputForecastedFiveDayVwapPerShareOfCommonStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputForecastedFiveDayVwapPerShareOfCommonStockMember" xlink:to="cntm_MeasurementInputForecastedFiveDayVwapPerShareOfCommonStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputForecastedFiveDayVwapPerShareOfCommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using forecasted five day VWAP per share of common stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputForecastedFiveDayVwapPerShareOfCommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Forecasted Five Day Vwap Per Share Of Common Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputForecastedFiveDayVwapPerShareOfCommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Forecasted five day VWAP per share of Company's common stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ResetDateMember" xlink:label="cntm_ResetDateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ResetDateMember" xlink:to="cntm_ResetDateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ResetDateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to scenario, reset date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ResetDateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reset Date [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ResetDateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reset date</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FirstResetDateMember" xlink:label="cntm_FirstResetDateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FirstResetDateMember" xlink:to="cntm_FirstResetDateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FirstResetDateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to scenario, first reset date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FirstResetDateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">First Reset Date [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FirstResetDateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">First reset date</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SecondResetDateMember" xlink:label="cntm_SecondResetDateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SecondResetDateMember" xlink:to="cntm_SecondResetDateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SecondResetDateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to scenario, first reset date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SecondResetDateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second Reset Date [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SecondResetDateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second reset date</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputPrepaymentRateMember" xlink:label="us-gaap_MeasurementInputPrepaymentRateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MeasurementInputPrepaymentRateMember" xlink:to="us-gaap_MeasurementInputPrepaymentRateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MeasurementInputPrepaymentRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Prepayment Rate [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MeasurementInputPrepaymentRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepayment premium</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ScenarioLatePaymentInObligationsMember" xlink:label="cntm_ScenarioLatePaymentInObligationsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ScenarioLatePaymentInObligationsMember" xlink:to="cntm_ScenarioLatePaymentInObligationsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ScenarioLatePaymentInObligationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to scenario where company is late in payment of debt obligation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ScenarioLatePaymentInObligationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Scenario, Late Payment In Obligations [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ScenarioLatePaymentInObligationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Scenario, Late payment of debt obligation</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_YaIiPnLtdYorkvilleMember" xlink:label="cntm_YaIiPnLtdYorkvilleMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_YaIiPnLtdYorkvilleMember" xlink:to="cntm_YaIiPnLtdYorkvilleMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_YaIiPnLtdYorkvilleMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to YA II PN, LTD (Yorkville)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_YaIiPnLtdYorkvilleMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ya Ii Pn, Ltd (Yorkville) [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_YaIiPnLtdYorkvilleMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">YA II PN, LTD (Yorkville)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentRiskAxis" xlink:label="us-gaap_DerivativeInstrumentRiskAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeInstrumentRiskAxis" xlink:to="us-gaap_DerivativeInstrumentRiskAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeInstrumentRiskAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Instrument [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeContractTypeDomain" xlink:label="us-gaap_DerivativeContractTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeContractTypeDomain" xlink:to="us-gaap_DerivativeContractTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeContractTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Contract [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockOptionMember" xlink:label="us-gaap_StockOptionMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockOptionMember" xlink:to="us-gaap_StockOptionMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockOptionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Option [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockOptionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchased Put Option</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertiblePromissoryNotesTrancheOneMember" xlink:label="cntm_ConvertiblePromissoryNotesTrancheOneMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertiblePromissoryNotesTrancheOneMember" xlink:to="cntm_ConvertiblePromissoryNotesTrancheOneMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertiblePromissoryNotesTrancheOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to convertible promissory notes, tranche one.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertiblePromissoryNotesTrancheOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Promissory Notes, Tranche One [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertiblePromissoryNotesTrancheOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible promissory notes (Tranche One)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertiblePromissoryNotesTrancheTwoMember" xlink:label="cntm_ConvertiblePromissoryNotesTrancheTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertiblePromissoryNotesTrancheTwoMember" xlink:to="cntm_ConvertiblePromissoryNotesTrancheTwoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertiblePromissoryNotesTrancheTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to convertible promissory notes, tranche two.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertiblePromissoryNotesTrancheTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Promissory Notes, Tranche Two [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertiblePromissoryNotesTrancheTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible promissory notes (Tranche Two)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EquityCommitmentMaximumLiability" xlink:label="cntm_EquityCommitmentMaximumLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquityCommitmentMaximumLiability" xlink:to="cntm_EquityCommitmentMaximumLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquityCommitmentMaximumLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of maximum equity commitment being the right, but not obligation, to sell the shares.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquityCommitmentMaximumLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Commitment, Maximum Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EquityCommitmentMaximumLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum equity commitment, being right but not obligation to sell share</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeTermOfContract" xlink:label="us-gaap_DerivativeTermOfContract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeTermOfContract" xlink:to="us-gaap_DerivativeTermOfContract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeTermOfContract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Term of Contract</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeTermOfContract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative term (in years)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentDiscountRatePercentageOfPrincipalAmount" xlink:label="cntm_DebtInstrumentDiscountRatePercentageOfPrincipalAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentDiscountRatePercentageOfPrincipalAmount" xlink:to="cntm_DebtInstrumentDiscountRatePercentageOfPrincipalAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentDiscountRatePercentageOfPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage discount rate on principal amount of debt.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentDiscountRatePercentageOfPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Discount Rate, Percentage Of Principal Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentDiscountRatePercentageOfPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Discount percentage (% on principal amount)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentNumberOfTranches" xlink:label="cntm_DebtInstrumentNumberOfTranches" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentNumberOfTranches" xlink:to="cntm_DebtInstrumentNumberOfTranches_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentNumberOfTranches_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of tranches in issue of convertible promissory notes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentNumberOfTranches_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Number Of Tranches</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentNumberOfTranches_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of tranches in issue of convertible promissory notes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentConvertibleThresholdTradingDays" xlink:label="us-gaap_DebtInstrumentConvertibleThresholdTradingDays" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentConvertibleThresholdTradingDays" xlink:to="us-gaap_DebtInstrumentConvertibleThresholdTradingDays_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentConvertibleThresholdTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible, Threshold Trading Days</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentConvertibleThresholdTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of trading volume days prior to requesting an Advance (in days)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PurchasePriceOfCommonStockMultiplierPercentageOfLowestVolumeWeightedAveragePriceDuringThreeDayPricingPeriod" xlink:label="cntm_PurchasePriceOfCommonStockMultiplierPercentageOfLowestVolumeWeightedAveragePriceDuringThreeDayPricingPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PurchasePriceOfCommonStockMultiplierPercentageOfLowestVolumeWeightedAveragePriceDuringThreeDayPricingPeriod" xlink:to="cntm_PurchasePriceOfCommonStockMultiplierPercentageOfLowestVolumeWeightedAveragePriceDuringThreeDayPricingPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PurchasePriceOfCommonStockMultiplierPercentageOfLowestVolumeWeightedAveragePriceDuringThreeDayPricingPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of the lowest VWAP (Volume Weighted Average Price) during a three-day pricing period being the multiplier on market price of common stock to compute purchase price of common stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PurchasePriceOfCommonStockMultiplierPercentageOfLowestVolumeWeightedAveragePriceDuringThreeDayPricingPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase Price of Common Stock Multiplier, Percentage of Lowest Volume Weighted Average Price During Three Day Pricing Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PurchasePriceOfCommonStockMultiplierPercentageOfLowestVolumeWeightedAveragePriceDuringThreeDayPricingPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Market price multiplier (being the % of of the lowest VWAP during a three-day pricing period)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentConvertibleLimitationMaximumOwnershipPercentageOnEachAdvance" xlink:label="cntm_DebtInstrumentConvertibleLimitationMaximumOwnershipPercentageOnEachAdvance" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConvertibleLimitationMaximumOwnershipPercentageOnEachAdvance" xlink:to="cntm_DebtInstrumentConvertibleLimitationMaximumOwnershipPercentageOnEachAdvance_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConvertibleLimitationMaximumOwnershipPercentageOnEachAdvance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum percentage of ownership to be permitted under debt conversion limitation after conversion in each advance given.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConvertibleLimitationMaximumOwnershipPercentageOnEachAdvance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible Limitation, Maximum Ownership Percentage On Each Advance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConvertibleLimitationMaximumOwnershipPercentageOnEachAdvance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum ownership percentage allowed post each advance conversion (%)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentConvertibleLimitationMaximumOwnershipPercentageOnAggregateAdvances" xlink:label="cntm_DebtInstrumentConvertibleLimitationMaximumOwnershipPercentageOnAggregateAdvances" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentConvertibleLimitationMaximumOwnershipPercentageOnAggregateAdvances" xlink:to="cntm_DebtInstrumentConvertibleLimitationMaximumOwnershipPercentageOnAggregateAdvances_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentConvertibleLimitationMaximumOwnershipPercentageOnAggregateAdvances_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum percentage of ownership to be permitted under debt conversion limitation after conversion in aggregate of advances given.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentConvertibleLimitationMaximumOwnershipPercentageOnAggregateAdvances_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Convertible Limitation, Maximum Ownership Percentage On Aggregate Advances</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentConvertibleLimitationMaximumOwnershipPercentageOnAggregateAdvances_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum ownership percentage allowed post aggregate advances conversion (%)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtRelatedCommitmentFeesAndDebtIssuanceCosts" xlink:label="us-gaap_DebtRelatedCommitmentFeesAndDebtIssuanceCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtRelatedCommitmentFeesAndDebtIssuanceCosts" xlink:to="us-gaap_DebtRelatedCommitmentFeesAndDebtIssuanceCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtRelatedCommitmentFeesAndDebtIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Related Commitment Fees and Debt Issuance Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtRelatedCommitmentFeesAndDebtIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total commitment fee</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CommitmentFeePaidThroughIssuanceOfCommonStockPercentage" xlink:label="cntm_CommitmentFeePaidThroughIssuanceOfCommonStockPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommitmentFeePaidThroughIssuanceOfCommonStockPercentage" xlink:to="cntm_CommitmentFeePaidThroughIssuanceOfCommonStockPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommitmentFeePaidThroughIssuanceOfCommonStockPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of commitment fee paid by way of issuance of common stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommitmentFeePaidThroughIssuanceOfCommonStockPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitment Fee Paid Through Issuance Of Common Stock, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CommitmentFeePaidThroughIssuanceOfCommonStockPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of commitment fee</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CommitmentFeePaidInCashPercentage" xlink:label="cntm_CommitmentFeePaidInCashPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommitmentFeePaidInCashPercentage" xlink:to="cntm_CommitmentFeePaidInCashPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommitmentFeePaidInCashPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of commitment fee paid in cash.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommitmentFeePaidInCashPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitment Fee Paid In Cash, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CommitmentFeePaidInCashPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of commitment fee paid in cash</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_RepaymentOfAdvancesOrLoansToRelateLendersMaximumThresholdAmountOfPrepaidAdvances" xlink:label="cntm_RepaymentOfAdvancesOrLoansToRelateLendersMaximumThresholdAmountOfPrepaidAdvances" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_RepaymentOfAdvancesOrLoansToRelateLendersMaximumThresholdAmountOfPrepaidAdvances" xlink:to="cntm_RepaymentOfAdvancesOrLoansToRelateLendersMaximumThresholdAmountOfPrepaidAdvances_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_RepaymentOfAdvancesOrLoansToRelateLendersMaximumThresholdAmountOfPrepaidAdvances_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum threshold amount of pre-paid advances after which company can repay advances or loans to related lenders, as defined in the SEPA.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_RepaymentOfAdvancesOrLoansToRelateLendersMaximumThresholdAmountOfPrepaidAdvances_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayment of Advances Or Loans To Relate Lenders, Maximum Threshold Amount Of Prepaid Advances</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_RepaymentOfAdvancesOrLoansToRelateLendersMaximumThresholdAmountOfPrepaidAdvances_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum threshold amount of pre-paid advance on which company can repay advances or loans to related lenders</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentRepaymentPercentageOfNetProceedFromNewFinancingTransaction" xlink:label="cntm_DebtInstrumentRepaymentPercentageOfNetProceedFromNewFinancingTransaction" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRepaymentPercentageOfNetProceedFromNewFinancingTransaction" xlink:to="cntm_DebtInstrumentRepaymentPercentageOfNetProceedFromNewFinancingTransaction_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRepaymentPercentageOfNetProceedFromNewFinancingTransaction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of amounts of net proceeds from new financing transaction use to repay the existing debt obligation from Yorkville.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRepaymentPercentageOfNetProceedFromNewFinancingTransaction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Repayment, Percentage Of Net Proceed From New Financing Transaction</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRepaymentPercentageOfNetProceedFromNewFinancingTransaction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of net proceeds from new financing transaction, use to repay existing debt obligation from Yorkville</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentRepaymentPercentageOfNetProceedFromForwardPurchaseAgreement" xlink:label="cntm_DebtInstrumentRepaymentPercentageOfNetProceedFromForwardPurchaseAgreement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentRepaymentPercentageOfNetProceedFromForwardPurchaseAgreement" xlink:to="cntm_DebtInstrumentRepaymentPercentageOfNetProceedFromForwardPurchaseAgreement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentRepaymentPercentageOfNetProceedFromForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of amounts of net proceeds from Forward Purchase Agreement (FPA) use to repay the existing debt obligation from Yorkville.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentRepaymentPercentageOfNetProceedFromForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Repayment, Percentage Of Net Proceed From Forward Purchase Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentRepaymentPercentageOfNetProceedFromForwardPurchaseAgreement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of net proceeds from Forward Purchase Agreement (FPA), use to repay existing debt obligation from Yorkville</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseCost" xlink:label="us-gaap_OperatingLeaseCost" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseCost" xlink:to="us-gaap_OperatingLeaseCost_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortTermLeaseCost" xlink:label="us-gaap_ShortTermLeaseCost" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShortTermLeaseCost" xlink:to="us-gaap_ShortTermLeaseCost_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShortTermLeaseCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Short-Term Lease, Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShortTermLeaseCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Short-term lease costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseInterestExpense" xlink:label="us-gaap_FinanceLeaseInterestExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseInterestExpense" xlink:to="us-gaap_FinanceLeaseInterestExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseInterestExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Interest Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseInterestExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest on lease liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseCost" xlink:label="us-gaap_LeaseCost" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LeaseCost" xlink:to="us-gaap_LeaseCost_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LeaseCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lease, Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LeaseCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total lease costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Weighted Average Remaining Lease Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted-average remaining lease term, Operating leases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:label="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Weighted Average Remaining Lease Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted-average remaining lease term, Finance leases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:to="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Weighted Average Discount Rate, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted-average discount rate, Operating leases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:label="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:to="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Weighted Average Discount Rate, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted-average discount rate, Finance leases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:label="us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:to="us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Leases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Liability, to be Paid, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Liability, to be Paid, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Liability, to be Paid</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total undiscounted lease payments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:label="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:to="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Liability, Undiscounted Excess Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: imputed interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiability" xlink:label="us-gaap_FinanceLeaseLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiability" xlink:to="us-gaap_FinanceLeaseLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finance Lease, Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total lease liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:to="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Leases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total undiscounted lease payments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: imputed interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiability" xlink:label="us-gaap_OperatingLeaseLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiability" xlink:to="us-gaap_OperatingLeaseLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total lease liabilities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LesseeOperatingLeaseAndFinanceLeaseLiabilityToBePaidFiscalYearMaturityAbstract" xlink:label="cntm_LesseeOperatingLeaseAndFinanceLeaseLiabilityToBePaidFiscalYearMaturityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LesseeOperatingLeaseAndFinanceLeaseLiabilityToBePaidFiscalYearMaturityAbstract" xlink:to="cntm_LesseeOperatingLeaseAndFinanceLeaseLiabilityToBePaidFiscalYearMaturityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LesseeOperatingLeaseAndFinanceLeaseLiabilityToBePaidFiscalYearMaturityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">No definition available.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LesseeOperatingLeaseAndFinanceLeaseLiabilityToBePaidFiscalYearMaturityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease And Finance Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LesseeOperatingLeaseAndFinanceLeaseLiabilityToBePaidFiscalYearMaturityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lease liabilities maturities</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LesseeLeaseLiabilityToBePaidYearOne" xlink:label="cntm_LesseeLeaseLiabilityToBePaidYearOne" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LesseeLeaseLiabilityToBePaidYearOne" xlink:to="cntm_LesseeLeaseLiabilityToBePaidYearOne_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LesseeLeaseLiabilityToBePaidYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of lessee's undiscounted obligation for lease payment for operating and financing lease to be paid in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LesseeLeaseLiabilityToBePaidYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Lease Liability, to be Paid, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LesseeLeaseLiabilityToBePaidYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LesseeLeaseLiabilityToBePaidYearTwo" xlink:label="cntm_LesseeLeaseLiabilityToBePaidYearTwo" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LesseeLeaseLiabilityToBePaidYearTwo" xlink:to="cntm_LesseeLeaseLiabilityToBePaidYearTwo_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LesseeLeaseLiabilityToBePaidYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of lessee's undiscounted obligation for lease payment for operating lease and financing to be paid in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LesseeLeaseLiabilityToBePaidYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Lease Liability, to be Paid, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LesseeLeaseLiabilityToBePaidYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LesseeLeaseLiabilityToBePaidYearThree" xlink:label="cntm_LesseeLeaseLiabilityToBePaidYearThree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LesseeLeaseLiabilityToBePaidYearThree" xlink:to="cntm_LesseeLeaseLiabilityToBePaidYearThree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LesseeLeaseLiabilityToBePaidYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of lessee's undiscounted obligation for lease payment for operating and financing lease to be paid in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LesseeLeaseLiabilityToBePaidYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Lease Liability, to be Paid, Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_LesseeLeaseLiabilityToBePaidYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LesseeLeaseLiabilityToBePaid" xlink:label="cntm_LesseeLeaseLiabilityToBePaid" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LesseeLeaseLiabilityToBePaid" xlink:to="cntm_LesseeLeaseLiabilityToBePaid_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LesseeLeaseLiabilityToBePaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of lessee's undiscounted obligation for lease payment for operating lease and financing lease.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LesseeLeaseLiabilityToBePaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Lease Liability, to be Paid</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="cntm_LesseeLeaseLiabilityToBePaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total undiscounted lease payments</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_LesseeLeaseLiabilityUndiscountedExcessAmount" xlink:label="cntm_LesseeLeaseLiabilityUndiscountedExcessAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_LesseeLeaseLiabilityUndiscountedExcessAmount" xlink:to="cntm_LesseeLeaseLiabilityUndiscountedExcessAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LesseeLeaseLiabilityUndiscountedExcessAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of lessee's undiscounted obligation for lease payments in excess of discounted obligation for lease payments for operating and financing lease.</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_LesseeLeaseLiabilityUndiscountedExcessAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: imputed interest</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_LeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Present value of lessee's discounted obligation for lease payments from operating and financing lease.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_LeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lease Liability</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (Loss) from Continuing Operations before Income Taxes, Foreign</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Foreign</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredFederalStateAndLocalTaxExpenseBenefitAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xlink:label="us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xlink:to="us-gaap_DeferredForeignIncomeTaxExpenseBenefit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredForeignIncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Foreign Income Tax Expense (Benefit)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DeferredForeignIncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Foreign</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:to="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Income Tax Expense (Benefit)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total Deferred</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationTable" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectiveIncomeTaxRateReconciliationTable" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">INCOME TAXES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:label="us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:to="us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax Expense (Benefit), Effective Income Tax Rate Reconciliation, Amount [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:label="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:to="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation at Federal Statutory Income Tax Rate, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax Expense (Benefit) at statutory federal rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationNondeductibleExpense" xlink:label="us-gaap_IncomeTaxReconciliationNondeductibleExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxReconciliationNondeductibleExpense" xlink:to="us-gaap_IncomeTaxReconciliationNondeductibleExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxReconciliationNondeductibleExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxReconciliationNondeductibleExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-deductible items</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EffectiveIncomeTaxRateReconciliationNontaxableBargainPurchaseGainAmount" xlink:label="cntm_EffectiveIncomeTaxRateReconciliationNontaxableBargainPurchaseGainAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EffectiveIncomeTaxRateReconciliationNontaxableBargainPurchaseGainAmount" xlink:to="cntm_EffectiveIncomeTaxRateReconciliationNontaxableBargainPurchaseGainAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EffectiveIncomeTaxRateReconciliationNontaxableBargainPurchaseGainAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to non-taxable bargain purchase gain.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EffectiveIncomeTaxRateReconciliationNontaxableBargainPurchaseGainAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, Nontaxable Bargain Purchase Gain, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_EffectiveIncomeTaxRateReconciliationNontaxableBargainPurchaseGainAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-taxable bargain purchase gain</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:label="us-gaap_IncomeTaxReconciliationOtherAdjustments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:to="us-gaap_IncomeTaxReconciliationOtherAdjustments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxReconciliationOtherAdjustments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Others</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:label="us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:to="us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Changes in Valuation Allowance</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EffectiveIncomeTaxRateReconciliationLossOnExtinguishmentOfDebtAmount" xlink:label="cntm_EffectiveIncomeTaxRateReconciliationLossOnExtinguishmentOfDebtAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EffectiveIncomeTaxRateReconciliationLossOnExtinguishmentOfDebtAmount" xlink:to="cntm_EffectiveIncomeTaxRateReconciliationLossOnExtinguishmentOfDebtAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EffectiveIncomeTaxRateReconciliationLossOnExtinguishmentOfDebtPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to loss on extinguishment of debts.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EffectiveIncomeTaxRateReconciliationLossOnExtinguishmentOfDebtPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, Loss On Extinguishment Of Debt, Percent</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsShareBasedCompensationCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock based compensation</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DeferredTaxAssetsOperatingLeaseLiability" xlink:label="cntm_DeferredTaxAssetsOperatingLeaseLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DeferredTaxAssetsOperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Tax Assets, Operating Lease Liability</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DeferredTaxAssetsExcessInterestExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Tax Assets, Excess Interest Expense</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOther" xlink:label="us-gaap_DeferredTaxAssetsOther" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssetsIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Tax Liabilities, Intangible Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssetsIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:label="us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:to="us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Tax Liabilities, Property, Plant and Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fixed asset</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DeferredTaxLiabilitiesRightOfUseAssets" xlink:label="cntm_DeferredTaxLiabilitiesRightOfUseAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DeferredTaxLiabilitiesRightOfUseAssets" xlink:to="cntm_DeferredTaxLiabilitiesRightOfUseAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DeferredTaxLiabilitiesRightOfUseAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of deferred tax liability attributable to taxable temporary differences from right of use assets.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DeferredTaxLiabilitiesRightOfUseAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Tax Liabilities, Right Of Use Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_DeferredTaxLiabilitiesRightOfUseAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ROU</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesOther" xlink:label="us-gaap_DeferredTaxLiabilitiesOther" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredTaxLiabilitiesOther" xlink:to="us-gaap_DeferredTaxLiabilitiesOther_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredTaxLiabilitiesOther_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Tax Liabilities, Other</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DeferredTaxLiabilitiesOther_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxLiabilities" xlink:label="us-gaap_DeferredIncomeTaxLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredIncomeTaxLiabilities" xlink:to="us-gaap_DeferredIncomeTaxLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredIncomeTaxLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Income Tax Liabilities, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:label="us-gaap_DeferredIncomeTaxLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total deferred tax liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilities" xlink:label="us-gaap_DeferredTaxLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredTaxLiabilities" xlink:to="us-gaap_DeferredTaxLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredTaxLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Tax Liabilities, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:label="us-gaap_DeferredTaxLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net deferred tax asset/(liability)</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ShareIssuanceOnExtinguishmentOfVendorObligationsMember" xlink:label="cntm_ShareIssuanceOnExtinguishmentOfVendorObligationsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ShareIssuanceOnExtinguishmentOfVendorObligationsMember" xlink:to="cntm_ShareIssuanceOnExtinguishmentOfVendorObligationsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ShareIssuanceOnExtinguishmentOfVendorObligationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to issuance of shares on extinguishment of vendor obligations.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ShareIssuanceOnExtinguishmentOfVendorObligationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Issuance On Extinguishment Of Vendor Obligations [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ShareIssuanceOnExtinguishmentOfVendorObligationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extinguishment of Vendor Obligations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LitigationSettlementAmountAwardedFromOtherParty" xlink:label="us-gaap_LitigationSettlementAmountAwardedFromOtherParty" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LitigationSettlementAmountAwardedFromOtherParty" xlink:to="us-gaap_LitigationSettlementAmountAwardedFromOtherParty_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LitigationSettlementAmountAwardedFromOtherParty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Litigation Settlement, Amount Awarded from Other Party</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LitigationSettlementAmountAwardedFromOtherParty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Litigation settlement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LitigationSettlementExpense" xlink:label="us-gaap_LitigationSettlementExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LitigationSettlementExpense" xlink:to="us-gaap_LitigationSettlementExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LitigationSettlementExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Litigation Settlement, Fee Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LitigationSettlementExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Litigation settlement, services fee</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EmployeeRetentionTaxCredit" xlink:label="cntm_EmployeeRetentionTaxCredit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EmployeeRetentionTaxCredit" xlink:to="cntm_EmployeeRetentionTaxCredit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EmployeeRetentionTaxCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of employee retention tax credit.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EmployeeRetentionTaxCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Employee Retention Tax Credit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EmployeeRetentionTaxCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ERC credits</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimingOfTransferOfGoodOrServiceAxis" xlink:label="us-gaap_TimingOfTransferOfGoodOrServiceAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TimingOfTransferOfGoodOrServiceAxis" xlink:to="us-gaap_TimingOfTransferOfGoodOrServiceAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TimingOfTransferOfGoodOrServiceAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Timing of Transfer of Good or Service [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimingOfTransferOfGoodOrServiceDomain" xlink:label="us-gaap_TimingOfTransferOfGoodOrServiceDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TimingOfTransferOfGoodOrServiceDomain" xlink:to="us-gaap_TimingOfTransferOfGoodOrServiceDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TimingOfTransferOfGoodOrServiceDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Timing of Transfer of Good or Service [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransferredAtPointInTimeMember" xlink:label="us-gaap_TransferredAtPointInTimeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TransferredAtPointInTimeMember" xlink:to="us-gaap_TransferredAtPointInTimeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TransferredAtPointInTimeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transferred at Point in Time [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TransferredAtPointInTimeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recognized at a point in time</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransferredOverTimeMember" xlink:label="us-gaap_TransferredOverTimeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TransferredOverTimeMember" xlink:to="us-gaap_TransferredOverTimeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TransferredOverTimeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transferred over Time [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TransferredOverTimeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recognized over a period of time</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EquityMethodInvestmentOwnershipPercentageToBeAcquired" xlink:label="cntm_EquityMethodInvestmentOwnershipPercentageToBeAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquityMethodInvestmentOwnershipPercentageToBeAcquired" xlink:to="cntm_EquityMethodInvestmentOwnershipPercentageToBeAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquityMethodInvestmentOwnershipPercentageToBeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of ownership of common stock or equity participation to be acquired in the investee accounted for under the equity method of accounting.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquityMethodInvestmentOwnershipPercentageToBeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Ownership Percentage To Be Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EquityMethodInvestmentOwnershipPercentageToBeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of equity interest to be acquired</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_EquityMethodInvestmentNumberOfSharesIssuable" xlink:label="cntm_EquityMethodInvestmentNumberOfSharesIssuable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_EquityMethodInvestmentNumberOfSharesIssuable" xlink:to="cntm_EquityMethodInvestmentNumberOfSharesIssuable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_EquityMethodInvestmentNumberOfSharesIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issuable as a part of consideration to the investee accounted for under the equity method of accounting.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_EquityMethodInvestmentNumberOfSharesIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Number Of Shares Issuable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_EquityMethodInvestmentNumberOfSharesIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration in the form of shares</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PercentageOfGrossRevenueAsServiceFees" xlink:label="cntm_PercentageOfGrossRevenueAsServiceFees" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PercentageOfGrossRevenueAsServiceFees" xlink:to="cntm_PercentageOfGrossRevenueAsServiceFees_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PercentageOfGrossRevenueAsServiceFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of gross revenue that is entitled to be received as fees for providing services.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PercentageOfGrossRevenueAsServiceFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage Of Gross Revenue As Service Fees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PercentageOfGrossRevenueAsServiceFees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of gross revenue</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TypeOfArrangementAxis" xlink:label="us-gaap_TypeOfArrangementAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TypeOfArrangementAxis" xlink:to="us-gaap_TypeOfArrangementAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:to="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_GreentechRenewablesHeatPumpDistributionDealMember" xlink:label="cntm_GreentechRenewablesHeatPumpDistributionDealMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_GreentechRenewablesHeatPumpDistributionDealMember" xlink:to="cntm_GreentechRenewablesHeatPumpDistributionDealMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_GreentechRenewablesHeatPumpDistributionDealMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Greentech Renewables Heat Pump Distribution Deal.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_GreentechRenewablesHeatPumpDistributionDealMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Greentech Renewables Heat Pump Distribution Deal [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_GreentechRenewablesHeatPumpDistributionDealMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Greentech Renewables</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DistributionAgreementInitialPurchaseOrder" xlink:label="cntm_DistributionAgreementInitialPurchaseOrder" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DistributionAgreementInitialPurchaseOrder" xlink:to="cntm_DistributionAgreementInitialPurchaseOrder_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DistributionAgreementInitialPurchaseOrder_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of initial purchase order placed under the distribution agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DistributionAgreementInitialPurchaseOrder_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distribution Agreement, Initial Purchase Order</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DistributionAgreementInitialPurchaseOrder_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Initial purchase order</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DistributionAgreementSubsequentPurchaseOrder" xlink:label="cntm_DistributionAgreementSubsequentPurchaseOrder" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DistributionAgreementSubsequentPurchaseOrder" xlink:to="cntm_DistributionAgreementSubsequentPurchaseOrder_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DistributionAgreementSubsequentPurchaseOrder_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of subsequent purchase order placed under the distribution agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DistributionAgreementSubsequentPurchaseOrder_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distribution Agreement, Subsequent Purchase Order</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DistributionAgreementSubsequentPurchaseOrder_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent purchase order</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DistributionAgreementCumulativePurchaseOrder" xlink:label="cntm_DistributionAgreementCumulativePurchaseOrder" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DistributionAgreementCumulativePurchaseOrder" xlink:to="cntm_DistributionAgreementCumulativePurchaseOrder_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DistributionAgreementCumulativePurchaseOrder_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cumulative purchase order placed under the distribution agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DistributionAgreementCumulativePurchaseOrder_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distribution Agreement, Cumulative Purchase Order</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DistributionAgreementCumulativePurchaseOrder_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cumulative purchase order</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SaleOfBusinessAssetsConsideration" xlink:label="cntm_SaleOfBusinessAssetsConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SaleOfBusinessAssetsConsideration" xlink:to="cntm_SaleOfBusinessAssetsConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SaleOfBusinessAssetsConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of consideration transferred in asset sale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SaleOfBusinessAssetsConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Business Assets, Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SaleOfBusinessAssetsConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset sale consideration</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SaleOfBusinessAssetsConsiderationReceivable" xlink:label="cntm_SaleOfBusinessAssetsConsiderationReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SaleOfBusinessAssetsConsiderationReceivable" xlink:to="cntm_SaleOfBusinessAssetsConsiderationReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SaleOfBusinessAssetsConsiderationReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of consideration receivable in asset sale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SaleOfBusinessAssetsConsiderationReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Business Assets, Consideration Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SaleOfBusinessAssetsConsiderationReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration receivable in asset sale</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SaleOfBusinessAssetsConsiderationSubjectToHoldback" xlink:label="cntm_SaleOfBusinessAssetsConsiderationSubjectToHoldback" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SaleOfBusinessAssetsConsiderationSubjectToHoldback" xlink:to="cntm_SaleOfBusinessAssetsConsiderationSubjectToHoldback_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SaleOfBusinessAssetsConsiderationSubjectToHoldback_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of consideration receivable in asset sale, subject to hold-back provision tied to delivery of disclosures and transition of operations.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SaleOfBusinessAssetsConsiderationSubjectToHoldback_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Business Assets, Consideration Subject to Holdback</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SaleOfBusinessAssetsConsiderationSubjectToHoldback_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration receivable in asset sale, subject to hold-back provision</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_SaleOfBusinessAssetsTransitionSupportServicesPeriod" xlink:label="cntm_SaleOfBusinessAssetsTransitionSupportServicesPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_SaleOfBusinessAssetsTransitionSupportServicesPeriod" xlink:to="cntm_SaleOfBusinessAssetsTransitionSupportServicesPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_SaleOfBusinessAssetsTransitionSupportServicesPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The period for transition support services on sale of certain assets.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_SaleOfBusinessAssetsTransitionSupportServicesPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Business Assets, Transition Support Services Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_SaleOfBusinessAssetsTransitionSupportServicesPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transition support services</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_UnsecuredConvertiblePromissoryNotesIssuedToInvestorsMember" xlink:label="cntm_UnsecuredConvertiblePromissoryNotesIssuedToInvestorsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_UnsecuredConvertiblePromissoryNotesIssuedToInvestorsMember" xlink:to="cntm_UnsecuredConvertiblePromissoryNotesIssuedToInvestorsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_UnsecuredConvertiblePromissoryNotesIssuedToInvestorsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to unsecured convertible promissory notes issued to investors.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_UnsecuredConvertiblePromissoryNotesIssuedToInvestorsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unsecured Convertible Promissory Notes Issued To Investors [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_UnsecuredConvertiblePromissoryNotesIssuedToInvestorsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unsecured convertible promissory notes issued to investors</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertiblePromissoryNotesWithAggregatePrincipalOf850000Member" xlink:label="cntm_ConvertiblePromissoryNotesWithAggregatePrincipalOf850000Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertiblePromissoryNotesWithAggregatePrincipalOf850000Member" xlink:to="cntm_ConvertiblePromissoryNotesWithAggregatePrincipalOf850000Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertiblePromissoryNotesWithAggregatePrincipalOf850000Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to convertible promissory note with aggregate principal principal of $850,000.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertiblePromissoryNotesWithAggregatePrincipalOf850000Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Promissory Notes With Aggregate Principal Of $850,000 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertiblePromissoryNotesWithAggregatePrincipalOf850000Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Four convertible promissory note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertiblePromissoryNotesAggregatePrincipalOf228000Member" xlink:label="cntm_ConvertiblePromissoryNotesAggregatePrincipalOf228000Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertiblePromissoryNotesAggregatePrincipalOf228000Member" xlink:to="cntm_ConvertiblePromissoryNotesAggregatePrincipalOf228000Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertiblePromissoryNotesAggregatePrincipalOf228000Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to one convertible promissory note with principal of $228,000.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertiblePromissoryNotesAggregatePrincipalOf228000Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Promissory Notes Aggregate Principal Of $228,000 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertiblePromissoryNotesAggregatePrincipalOf228000Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">One convertible promissory note</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfDebtInstrumentsIssued" xlink:label="cntm_NumberOfDebtInstrumentsIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfDebtInstrumentsIssued" xlink:to="cntm_NumberOfDebtInstrumentsIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfDebtInstrumentsIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the number of debt instruments issued.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfDebtInstrumentsIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Debt Instruments Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfDebtInstrumentsIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of debt instruments issued</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PromissoryNotesAndTermLoanMember" xlink:label="cntm_PromissoryNotesAndTermLoanMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PromissoryNotesAndTermLoanMember" xlink:to="cntm_PromissoryNotesAndTermLoanMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PromissoryNotesAndTermLoanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to promissory notes and term loan.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PromissoryNotesAndTermLoanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Promissory Notes And Term loan [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PromissoryNotesAndTermLoanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Promissory note and term loan</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PromissoryNoteThreeMember" xlink:label="cntm_PromissoryNoteThreeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PromissoryNoteThreeMember" xlink:to="cntm_PromissoryNoteThreeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PromissoryNoteThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to promissory note, three.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PromissoryNoteThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Promissory Note, Three [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PromissoryNoteThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Promissory note, three</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_PromissoryNoteFourMember" xlink:label="cntm_PromissoryNoteFourMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_PromissoryNoteFourMember" xlink:to="cntm_PromissoryNoteFourMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_PromissoryNoteFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to promissory note, four.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_PromissoryNoteFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Promissory Note, Four [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_PromissoryNoteFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Promissory note, four</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_TermLoanOneMember" xlink:label="cntm_TermLoanOneMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_TermLoanOneMember" xlink:to="cntm_TermLoanOneMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_TermLoanOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to term loan, one.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_TermLoanOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term Loan, One [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_TermLoanOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term loan, one</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_TermLoanTwoMember" xlink:label="cntm_TermLoanTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_TermLoanTwoMember" xlink:to="cntm_TermLoanTwoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_TermLoanTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to term loan, two.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_TermLoanTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term Loan, Two [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_TermLoanTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term loan, two</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NumberOfDebtInstrumentsModified" xlink:label="cntm_NumberOfDebtInstrumentsModified" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NumberOfDebtInstrumentsModified" xlink:to="cntm_NumberOfDebtInstrumentsModified_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NumberOfDebtInstrumentsModified_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of debt instruments modified during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NumberOfDebtInstrumentsModified_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Debt Instruments Modified</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_NumberOfDebtInstrumentsModified_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of debt instruments modified</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_MerchantCashAdvancesMember" xlink:label="cntm_MerchantCashAdvancesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MerchantCashAdvancesMember" xlink:to="cntm_MerchantCashAdvancesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MerchantCashAdvancesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to merchant cash advances.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MerchantCashAdvancesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Merchant Cash Advances [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MerchantCashAdvancesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Merchant cash advances</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentTotalRepaymentAmount" xlink:label="cntm_DebtInstrumentTotalRepaymentAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentTotalRepaymentAmount" xlink:to="cntm_DebtInstrumentTotalRepaymentAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentTotalRepaymentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of the total periodic payments including both interest and principal payments.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentTotalRepaymentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Total Repayment Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentTotalRepaymentAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total repayment amount</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_DebtInstrumentOriginationFee" xlink:label="cntm_DebtInstrumentOriginationFee" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_DebtInstrumentOriginationFee" xlink:to="cntm_DebtInstrumentOriginationFee_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_DebtInstrumentOriginationFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of origination fees associated with the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_DebtInstrumentOriginationFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Origination Fee</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_DebtInstrumentOriginationFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Origination fees</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ReverseStockSplitTable" xlink:label="cntm_ReverseStockSplitTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ReverseStockSplitTable" xlink:to="cntm_ReverseStockSplitTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ReverseStockSplitTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of information about reverse stock split.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ReverseStockSplitTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reverse Stock Split [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ReverseStockSplitTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reverse Stock Split [Table]</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ReverseStockSplitLine" xlink:label="cntm_ReverseStockSplitLine" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ReverseStockSplitLine" xlink:to="cntm_ReverseStockSplitLine_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ReverseStockSplitLine_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ReverseStockSplitLine_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reverse Stock Split [Line]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ReverseStockSplitLine_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REVERSE STOCK SPLIT</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CommonStockSharesIssuedBeforeReverseStockSplit" xlink:label="cntm_CommonStockSharesIssuedBeforeReverseStockSplit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommonStockSharesIssuedBeforeReverseStockSplit" xlink:to="cntm_CommonStockSharesIssuedBeforeReverseStockSplit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommonStockSharesIssuedBeforeReverseStockSplit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of common stock issued before reverse stock split.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommonStockSharesIssuedBeforeReverseStockSplit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Issued, Before Reverse Stock Split</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CommonStockSharesIssuedBeforeReverseStockSplit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock issued, Pre-Split</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CommonStockSharesIssuedAfterReverseStockSplit" xlink:label="cntm_CommonStockSharesIssuedAfterReverseStockSplit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommonStockSharesIssuedAfterReverseStockSplit" xlink:to="cntm_CommonStockSharesIssuedAfterReverseStockSplit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommonStockSharesIssuedAfterReverseStockSplit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of common stock issued after reverse stock split.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommonStockSharesIssuedAfterReverseStockSplit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Issued, After Reverse Stock Split</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CommonStockSharesIssuedAfterReverseStockSplit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock issued, Post-Split</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CommonStockSharesOutstandingBeforeReverseStockSplit" xlink:label="cntm_CommonStockSharesOutstandingBeforeReverseStockSplit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommonStockSharesOutstandingBeforeReverseStockSplit" xlink:to="cntm_CommonStockSharesOutstandingBeforeReverseStockSplit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommonStockSharesOutstandingBeforeReverseStockSplit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of common stock outstanding before reverse stock split.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommonStockSharesOutstandingBeforeReverseStockSplit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Outstanding, Before Reverse Stock Split</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CommonStockSharesOutstandingBeforeReverseStockSplit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock outstanding, Pre-Split</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_CommonStockSharesOutstandingAfterReverseStockSplit" xlink:label="cntm_CommonStockSharesOutstandingAfterReverseStockSplit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_CommonStockSharesOutstandingAfterReverseStockSplit" xlink:to="cntm_CommonStockSharesOutstandingAfterReverseStockSplit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_CommonStockSharesOutstandingAfterReverseStockSplit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares of common stock outstanding after reverse stock split.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_CommonStockSharesOutstandingAfterReverseStockSplit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Outstanding, After Reverse Stock Split</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_CommonStockSharesOutstandingAfterReverseStockSplit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock outstanding, Post-Split</label>
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