Tcr2 Therapeutics (TCRR) 10-Q 2021 Q1 Quarterly report

Exhibit 32.1

CERTIFICATIONS OF PRINCIPAL EXECUTIVE OFFICER AND PRINCIPAL

FINANCIAL OFFICER PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES‑OXLEY ACT OF 2002

In connection with this Quarterly Report on Form 10‑Q of TCR² Therapeutics Inc. (the “Company”) for the period ended March 31, 2021 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), each of the undersigned, hereby certifies, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes‑Oxley Act of 2002, that, to the best of his or her 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 Company.

Dated: May 13, 2021

/s/ Garry E. Menzel

Garry E. Menzel

President, Chief Executive Officer and Director

(Principal Executive Officer)

/s/ Mayur (Ian) Somaiya

Mayur (Ian) Somaiya

Chief Financial Officer

(Principal Financial Officer and Accounting Officer)