N.M. Stat. § 19-4-24
Whenever complaint shall be filed in any such action, summons shall be issued against the proper parties, and served upon the person or persons named therein, as in other cases provided by law, or upon the agent or attorney of such person or persons who shall have filed their statements as required by Section 19-4-10 NMSA 1978. And in case service cannot be had upon the defendants, their agents or attorney, the complainant shall file an affidavit in the office of the clerk of the court in which the action in [is] pending, to the effect and as now provided by law. It shall be lawful for the clerk of said court to cause publication to be made as provided by law, and when such publication shall have been made, the cause shall proceed, as if the parties had been personally served with summons.
NMS § 19-4-24