N.M. Stat. § 19-4-23
In case suits shall not be brought for the purpose of settling or determining any controversy to any such lands by either of the adverse claimants, within sixty days after the expiration of the time for filing the statement, as provided in Section 19-4-10 NMSA 1978, it shall be the duty of the probate judge or corporate authorities to give notice to the adverse claimant filing his claim, or, if there be more than one adverse claim filed, then to the last adverse claimant, directing him to commence his action against the other claimants, as defendants, to determine their respective rights to said lands, within twenty days from service of notice on him, and in case such adverse claimant neglect or refuse to commence the action within the time specified, he shall be deemed to have relinquished all right, title, interest and estate in the lands so in controversy, and be forever barred from asserting or claiming any right, title, interest or estate, therein. Such notice shall be served by the proper officer of said courts, in the same manner as now provided for service of summons in any county in this state. If the officer return such notice, not found, notice shall be made by publication for three weeks in some newspaper published in the county where the lands are situated, and if no paper be published in said county, then by posting such notice in three public places in the town where such lands are situated. And in addition thereto a copy of said notice shall be mailed to such adverse claimant at his residence or usual place of abode. And in case there be more than one adverse claimant, and the last neglect or refuse to commence his action after service of notice, as aforesaid, said probate judge or corporate authorities shall serve like notice on the next last adverse claimants, until all have been notified, as aforesaid.
NMS § 19-4-23