N.M. Stat. § 10-5-4
The secretary of finance and administration is authorized to administer oaths to persons who testify at such hearing. The secretary may compel the attendance of any person whose testimony may be required or needed at such hearing, and to compel the production of books, papers, documents, records and data necessary thereto. The official requesting the hearing shall have the right to make timely request to the secretary that subpoenas for necessary and material witnesses or for the production of documents and papers be issued, and the same shall be issued. The secretary and such employees of the department as may be designated by the secretary are authorized to issue subpoenas for persons whose testimony is required, and subpoenas so issued shall be served by persons authorized by law to make such service in civil actions, and if served by a sheriff or deputy, such service shall be made without cost.
NMS § 10-5-4