N.M. Stat. § 73-7-34
If it shall appear at any time that any tract or parcel of land covered by a certificate of sale held by any county acquired by it at general tax sale for taxes and/or drainage assessments cannot be sold for the amount of the accumulated taxes and assessments against the same, an action may be instituted upon petition to the district court by such district to inquire as to the value of such lands, and a copy of such petition shall be served upon the property tax division of the taxation and revenue department and upon the collector and treasurer of the county in which such lands are situated. If it shall appear upon the hearing of such petition that the lands cannot be sold for the amount of all accumulated general taxes and assessments against such lands, then the court shall order such lands sold as the court may direct at public sale after four weeks' notice by publication, for the best price obtainable, free and clear of all such taxes and assessments, but the owner or anyone interested in the title may redeem from such sale as provided in Section 73-7-31 NMSA 1978. The proceeds of such sale shall be divided pro rata between the county treasurer and the treasurer of said district in discharge of such taxes and assessments.
NMS § 73-7-34