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<!--Created on: 5/26/2026 5:34:51 PM-->
<!--Modified on: 5/26/2026 5:34:51 PM-->
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsAbstract" xlink:to="us-gaap_AssetsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsCurrentAbstract" xlink:to="us-gaap_AssetsCurrentAbstract_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_AssetsCurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and Cash Equivalents, at Carrying Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_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_AccountsReceivableNetCurrent" xlink:label="us-gaap_AccountsReceivableNetCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableNetCurrent" xlink:to="us-gaap_AccountsReceivableNetCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, after Allowance for Credit Loss, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable - net of allowance for credit loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of standard support services owed from related party</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerAssetNetCurrent" xlink:label="us-gaap_ContractWithCustomerAssetNetCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractWithCustomerAssetNetCurrent" xlink:to="us-gaap_ContractWithCustomerAssetNetCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractWithCustomerAssetNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Asset, after Allowance for Credit Loss, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ContractWithCustomerAssetNetCurrent_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_InventoryNet" xlink:label="us-gaap_InventoryNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <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_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>
    <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>
    <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>
    <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/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>
    <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>
    <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>
    <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="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/2003/role/terseLabel" xlink:label="us-gaap_DeferredIncomeTaxLiabilities_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>
    <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>
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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>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity, Including Portion Attributable to Noncontrolling Interest</label>
    <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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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total stockholders' deficit</label>
    <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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    <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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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SeriesAPreferredStockMember" xlink:to="us-gaap_SeriesAPreferredStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <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>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SeriesAPreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock Series A</label>
    <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/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" />
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    <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/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" />
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    <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>
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    <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>
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    <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>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity Note, Stock Split, Conversion Ratio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reverse stock split</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementAbstract" xlink:label="us-gaap_IncomeStatementAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeStatementAbstract" xlink:to="us-gaap_IncomeStatementAbstract_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_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_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_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>
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    <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/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>
    <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_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/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_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/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>
    <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" />
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    <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" />
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    <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>
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    <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" />
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    <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>
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    <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" />
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    <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" />
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    <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>
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    <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" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest</label>
    <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>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTax" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive 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_WeightedAverageNumberOfSharesOutstandingBasic" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xmlns="http://www.xbrl.org/2003/linkbase" />
    <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" />
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    <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_EarningsPerShareBasic" xlink:label="us-gaap_EarningsPerShareBasic" 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_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_StatementOfStockholdersEquityAbstract" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract" 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_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" />
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    <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_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>
    <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>
    <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>
    <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>
    <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/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_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>
    <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>
    <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="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>
    <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_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/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="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_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt" xlink:label="cntm_IncreaseDecreaseInGainLossOnFairValueMeasurementOfConvertibleDebt" 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_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" />
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    <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>
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    <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="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="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/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_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_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>
    <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>
    <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="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_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="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="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_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>
    <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>
    <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="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>
    <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" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsAbstract" xlink:to="us-gaap_RelatedPartyTransactionsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <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>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transactions Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_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_CommitmentsAndContingenciesDisclosureAbstract" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_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_CommitmentsAndContingenciesDisclosureTextBlock" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments and Contingencies Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_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_RevenueFromContractWithCustomerAbstract" xlink:label="us-gaap_RevenueFromContractWithCustomerAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerAbstract" xlink:to="us-gaap_RevenueFromContractWithCustomerAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromContractWithCustomerAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REVENUES</label>
    <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" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:to="us-gaap_RevenueFromContractWithCustomerTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromContractWithCustomerTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue from Contract with Customer [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REVENUES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureAbstract" xlink:label="us-gaap_IncomeTaxDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxDisclosureAbstract" xlink:to="us-gaap_IncomeTaxDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxDisclosureAbstract_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_IncomeTaxDisclosureTextBlock" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_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_SegmentReportingAbstract" xlink:label="us-gaap_SegmentReportingAbstract" 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_SegmentReportingAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REPORTABLE SEGMENTS</label>
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    <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" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventsAbstract" xlink:to="us-gaap_SubsequentEventsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <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>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsTextBlock" xlink:label="us-gaap_SubsequentEventsTextBlock" 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_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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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basis of presentation and principles of consolidation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UseOfEstimates" xlink:label="us-gaap_UseOfEstimates" 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_UseOfEstimates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Use of Estimates, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UseOfEstimates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Use of estimates</label>
    <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" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:to="us-gaap_SegmentReportingPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <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>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryPolicyTextBlock" xlink:label="us-gaap_InventoryPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryPolicyTextBlock" xlink:to="us-gaap_InventoryPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventories</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_NonControllingInterestPolicyTextBlock" xlink:label="cntm_NonControllingInterestPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_NonControllingInterestPolicyTextBlock" xlink:to="cntm_NonControllingInterestPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_NonControllingInterestPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for Non-controlling Interest.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_NonControllingInterestPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-Controlling Interest [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_NonControllingInterestPolicyTextBlock_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_EquityMethodInvestmentsPolicy" xlink:label="us-gaap_EquityMethodInvestmentsPolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentsPolicy" xlink:to="us-gaap_EquityMethodInvestmentsPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investments [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity method investment</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_BusinessCombinationAndAssetAcquisitionPolicyPolicyTextBlock" xlink:label="cntm_BusinessCombinationAndAssetAcquisitionPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_BusinessCombinationAndAssetAcquisitionPolicyPolicyTextBlock" xlink:to="cntm_BusinessCombinationAndAssetAcquisitionPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_BusinessCombinationAndAssetAcquisitionPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for business combination and asset acquisition.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_BusinessCombinationAndAssetAcquisitionPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination and Asset Acquisition Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_BusinessCombinationAndAssetAcquisitionPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination and asset acquisition</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerSharePolicyTextBlock" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerSharePolicyTextBlock" xlink:to="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss per share</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_ConvertibleNotesPayablePolicyTextBlock" xlink:label="cntm_ConvertibleNotesPayablePolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_ConvertibleNotesPayablePolicyTextBlock" xlink:to="cntm_ConvertibleNotesPayablePolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_ConvertibleNotesPayablePolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for convertible notes payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_ConvertibleNotesPayablePolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Notes Payable [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_ConvertibleNotesPayablePolicyTextBlock_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_StockholdersEquityPolicyTextBlock" xlink:label="us-gaap_StockholdersEquityPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityPolicyTextBlock" xlink:to="us-gaap_StockholdersEquityPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockholdersEquityPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reverse Stock Split</label>
    <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" />
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    <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" />
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    <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" />
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    <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="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" />
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    <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="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" />
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    <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>
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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>
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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_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>
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    <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_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="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>
    <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="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>
    <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="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/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>
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    <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>
    <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>
    <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>
    <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/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_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>
    <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="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="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" />
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    <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>
    <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>
    <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>
    <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>
    <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="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentAxis" xlink:label="us-gaap_DebtInstrumentAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <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="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_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="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="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>
    <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/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>
    <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_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>
    <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="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_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_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_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>
    <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/2003/role/terseLabel" 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/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_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>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cntm_GlobalImpexLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Geo Impex</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="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="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_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_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_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:label="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <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_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="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>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Settlements, Stock Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlementsStockIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement through issuance of Company's common stock</label>
    <loc xlink:type="locator" xlink:href="cntm-20260331.xsd#cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnExtinguishmentAndChangeInFairValueOfConvertibleDebt" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnExtinguishmentAndChangeInFairValueOfConvertibleDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnExtinguishmentAndChangeInFairValueOfConvertibleDebt" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnExtinguishmentAndChangeInFairValueOfConvertibleDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnExtinguishmentAndChangeInFairValueOfConvertibleDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain (loss) on extinguishment and change in fair value of convertible debt liability 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_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnExtinguishmentAndChangeInFairValueOfConvertibleDebt_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 And Change In Fair Value Of Convertible Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnExtinguishmentAndChangeInFairValueOfConvertibleDebt_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_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnIssuanceOfFinancialInstruments" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnIssuanceOfFinancialInstruments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnIssuanceOfFinancialInstruments" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnIssuanceOfFinancialInstruments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <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>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossOnIssuanceOfFinancialInstruments_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_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisReclassification" xlink:label="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisReclassification" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisReclassification" xlink:to="cntm_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisReclassification_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <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" />
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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" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MeasurementInputDiscountRateMember" xlink:to="us-gaap_MeasurementInputDiscountRateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MeasurementInputDiscountRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Discount Rate [Member]</label>
    <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>
    <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" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember" xlink:to="cntm_MeasurementInputProbabilityOfVoluntaryConversionScenarioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <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>
    <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>
    <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" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cntm_MeasurementInputRemainingTermForVoluntaryConversionScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement input using remaining term for voluntary conversion scenario.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cntm_MeasurementInputRemainingTermForVoluntaryConversionScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input, Remaining Term For Voluntary Conversion Scenario [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cntm_MeasurementInputRemainingTermForVoluntaryConversionScenarioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining term for voluntary conversion scenario</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" 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" />
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    <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" />
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    <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="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="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/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/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/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/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="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_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_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="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/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>
    <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>
    <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="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_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_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.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">Chatrapur, Odisha, India</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="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxContingencyTable" xlink:label="us-gaap_IncomeTaxContingencyTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxContingencyTable" xlink:to="us-gaap_IncomeTaxContingencyTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxContingencyTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax Contingency [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxContingencyLineItems" xlink:label="us-gaap_IncomeTaxContingencyLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxContingencyLineItems" xlink:to="us-gaap_IncomeTaxContingencyLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxContingencyLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax Contingency [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxContingencyLineItems_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_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Federal statutory rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Segment Reporting Information, by Segment [Table]</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.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_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>
    <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_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="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_ConcentrationRiskByTypeAxis" xlink:label="us-gaap_ConcentrationRiskByTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskByTypeAxis" xlink:to="us-gaap_ConcentrationRiskByTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskByTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Type [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskTypeDomain" xlink:label="us-gaap_ConcentrationRiskTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskTypeDomain" xlink:to="us-gaap_ConcentrationRiskTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <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_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>
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    <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" />
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    <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" />
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    <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" />
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    <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" />
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    <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>
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    <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>
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