Exhibit 32.1

Certification Pursuant To 18 U.S.C. Section 1350 As Adopted Pursuant To Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Quarterly Report of HMS Holdings Corp. (the “Company”) on Form 10-Q for the period ended September 30, 2019 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, William C. Lucia, Chief Executive Officer of the Company, hereby certify, to the best of my knowledge, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

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

(2)the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ William C. Lucia

William C. Lucia

Chief Executive Officer

(Principal Executive Officer)

November 4, 2019