Steadfast Apartment REIT III 10-Q 2019 Q1 Quarterly report

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

     Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 and in connection with the Quarterly Report on Form 10-Q of Steadfast Apartment REIT III, Inc. (the “Company”) for the period ended March 31, 2019, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), the undersigned, the Principal Executive Officer of the Company, certifies, to his knowledge, 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.

Date: May 10, 2019

By:	/s/ Rodney F. Emery
	Rodney F. Emery
	Chief Executive Officer and Chairman of the Board (Principal Executive Officer)