N.M. Stat. § 19-4-13
The board of trustees of any such town shall appoint, by order, resolution or ordinance, a board of appraisers, to consist of three freeholders of any such town, who shall have no interest in such unclaimed or unconveyed lots, or parcels of land, or the improvements thereon. Each of said appraisers shall take an oath to faithfully discharge his duties as such appraiser, and shall file such oath in the office of the clerk of said board before commencing his duties as such appraiser. In case such appraisers should fail or neglect to make the appraisement hereinafter specified in this chapter [19-4-14 NMSA 1978], and file the same with the clerk of said board, for a period of more than ten days after their appointment, then said board may appoint a new board of appraisers for the purposes herein provided. It shall be the duty of such board to appoint such appraisers within thirty days after the time has expired for persons to present claims for lots in such towns.
NMS § 19-4-13