N.M. Stat. § 39-5-7
For that purpose two disinterested householders of the neighborhood where the levy is made shall be selected as appraisers, one of whom shall be selected by each of the parties or their agents, or in the absence of either party or his agent, or upon the refusal of either party, after three days' notice by the sheriff to make the selection, the sheriff shall proceed to select the appraisers, who shall proceed to appraise the property according to its cash value at the time, deducting liens and encumbrances; and in case of their disagreement as to the value thereof, they shall select a like disinterested appraiser, and with his assistance shall complete the valuation, and the appraisement of any two of them shall be deemed the cash value.
NMS § 39-5-7