N.M. Stat. § 51-1-31

In the administration of the Unemployment Compensation Law the secretary shall cooperate to the fullest extent possible under the act with the United States secretary of labor in his duties under the Social Security Act, 42 U.S.C. Section 301 et seq., as amended. The secretary shall make reports in the form and containing such information as the secretary of labor may from time to time require, and shall comply with such provisions as the secretary of labor may from time to time find necessary to assure the correctness and verification of such reports. The department shall comply with regulations prescribed by the secretary of labor governing expenditures of such sums as may be allotted and paid to this state under Title 3 of the Social Security Act, 42 U.S.C. Sections 501 through 503 , for the purpose of assisting in the administration of the Unemployment Compensation Law.

Upon request, the secretary shall furnish to any agency of the United States charged with administration of public works or assistance through public employment, the name, address, ordinary occupation and employment status of each recipient of benefits, and such recipient's rights to further benefits under the Unemployment Compensation Law.