N.M. Stat. § 51-1-28
In discharging duties imposed by the Unemployment Compensation Law, [the] board of review or the secretary or his authorized representative has power to administer oaths and affirmations, take depositions, certify to official acts and issue subpoenas to compel attendance of witnesses and production of books, papers, correspondence, memoranda and other records deemed necessary as evidence in connection with a disputed claim or the administration of the Unemployment Compensation Law. Service of subpoenas may be made personally upon the party named therein or, at the option of the secretary, by registered mail with return receipt requested, addressed to the person to be served at his last known address. When service is made by registered mail the subpoena shall be posted not less than ten days prior to the return day. The registry return receipt of a person served by registered mail, accompanied by a certificate or affidavit of the person mailing the subpoena, constitutes proof of service.
NMS § 51-1-28