Exhibit 19(b)

CERTIFICATION

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

(Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code)

In connection with the annual report of Nuveen Multistate Trust III (the “Registrant”) on Form N-CSR for the period ended May 31, 2025, as filed with the Securities and Exchange Commission (the “Report”), the undersigned officers of the Registrant certify that, to the best of each such officer’s knowledge:

 

1.

The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

 

2.

The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Registrant.

 

Date: August 6, 2025		By:		/s/ Jordan M. Farris
				Jordan M. Farris Chief Administrative Officer (principal executive officer)
Date: August 6, 2025		By:		/s/ Marc Cardella
				Marc Cardella Vice President and Controller (principal financial officer)