N.M. Stat. § 4-33-17
If there are no qualified electors residing within the portion of a county proposed to be annexed by another county, resolutions shall be passed by the county commissions of both affected counties approving a transfer of territory from one county to the other. The resolutions shall state the facts permitting such transfer by this method and a description of the territory to be transferred. The county clerks shall forward a copy of each resolution to the secretary of state. The county to which the territory is to be transferred shall place the territory within one or more of its voting precincts and so notify the secretary of state for compliance with election laws. Any aggrieved property owner or qualified elector within the annexed territory may file an action in the district court; if no action is filed within the ninety days, the transfer of the territory shall take place in accordance with the provisions of Section 4-33-7 NMSA 1978.
NMS § 4-33-17