N.M. Stat. § 4-47-4
The judge of the district court shall appoint three appraisers to appraise such property proposed to be sold as specified in the preceding section and such appraisers shall make and return under oath an appraisement of the actual cash value of such property, and upon return of such appraisement to the district court, the board of commissioners shall proceed to advertise such property for public sale, giving at least three weeks' notice of the hour, time and place of such sale, which notice shall be inserted in some daily or weekly newspaper published in the city or town where such property is located, if one be published therein; if not, in some paper of general circulation therein, and shall cause such property to be offered for sale at the time stated in such notice; and such property shall not be sold for less than two-thirds of the appraised value, and it shall be the duty of such board to require the payment in cash of at least one-half of the purchase price of said property, and they shall require the purchaser in lieu of the remainder of the purchase price, to execute proper security for the amount of the same.
NMS § 4-47-4