United Development Funding III (UDF) 10-Q 2012 Q1 Quarterly report

Exhibit 32.1

SECTION 1350 CERTIFICATIONS

This Certificate is being delivered pursuant to the requirements of Section 1350 of Chapter 63 (Mail Fraud) of Title 18 (Crimes and Criminal Procedures) of the United States Code and shall not be relied on by any person for any other purpose.

The undersigned, who are (i) the Chief Executive Officer of UMTH Land Development, L.P., the general partner of United Development Funding III, L.P. (the “Partnership”), and (ii) the Chief Financial Officer of UMTH Land Development, L.P., the general partner of the Partnership, each hereby certify as follows:

The Quarterly Report on Form 10-Q of the Partnership (the “Report”), which accompanies this Certificate, fully complies with the requirements of Section 13(a) or Section 15(d), as applicable, of the Securities Exchange Act of 1934, as amended, and all information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Partnership.

Dated this 15th day of May, 2012.

/s/ Hollis M. Greenlaw

Hollis M. Greenlaw

Chief Executive Officer of UMTH Land Development, L.P., sole general partner of the Registrant, and President and Chief Executive Officer of UMT Services, Inc., sole general partner of UMTH Land Development, L.P.

/s/ Cara D. Obert

Cara D. Obert

Chief Financial Officer of UMTH Land Development, L.P., sole general partner of the Registrant

A signed original of this written statement required by Section 906 of the Sarbanes-Oxley Act of 2002 has been provided to the registrant and will be retained by the registrant and furnished to the Securities and Exchange Commission or its staff upon request.