N.M. Stat. § 3-51-18
Upon completion of the plans and cost estimates for the proposed project, the governing body of the city shall appoint a board of appraisers which shall consist of three appraisers, whose terms of office shall run until the appraisals of benefits and damages are filed in the office of the clerk of the city and rendered final by failure of the property owners to protest or by approval after hearing on the protest.
The duties of the board of appraisers shall be to appraise all benefits and damages accruing to all real property within or without the tentative boundaries of the district by reason of the making of the proposed project.
The governing body of the city by ordinance shall prescribe the qualifications and the compensation of the appraisers, the government of the board and methods for filling vacancies on the board or for the replacement of members of the board.
NMS § 3-51-18