Form 497J NUVEEN MULTISTATE TRUST

Filed pursuant to Rule 497(j)

Registration Nos. 333-14729 and 811-07755

[ON CHAPMAN AND CUTLER LLP LETTERHEAD]

June 30, 2022

Securities and Exchange Commission

100 F Street, N.E.

Washington, DC 20549

Ladies and Gentlemen:

On behalf of the Registrant, in accordance with the provisions of Rule 497(j) of Regulation C under the Securities Act of 1933 (the “Securities Act”), this letter serves to certify that the most recent amendment to the registration statement on Form N-1A (the “Registration Statement”) of the Registrant and its series, Nuveen California High Yield Municipal Bond Fund, Nuveen California Municipal Bond Fund, Nuveen Connecticut Municipal Bond Fund, Nuveen Massachusetts Municipal Bond Fund, Nuveen New Jersey Municipal Bond Fund and Nuveen New York Municipal Bond Fund, does not differ from that which would have been filed pursuant to Rule 497(c) of the Securities Act. Post-Effective Amendment No. 52, which was the most recent amendment to the Registration Statement, was filed electronically with the Securities and Exchange Commission on June 28, 2022.

If you have any questions or comments, please telephone the undersigned at (312) 845-3484.

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