New Mexico Statutes 73-21-15. Board increase; appointed members
A. In every district, three members of the board shall be elected by the qualified electors pursuant to the provisions of the Local Election Act [N.M. Stat. Ann. Chapter 1, Article 22].
B. In those districts that have five board members, the board may by resolution designate two board members to serve by appointment. In those districts that have three board members, the board may by resolution expand the board to include two appointed board members. A resolution adopted pursuant to this subsection shall not be rescinded until two regular local elections have passed after adoption of the resolution.
C. The appointment of board members serving pursuant to a resolution adopted pursuant to Subsection B of this section shall be for a term of two years beginning July 1 of each even-numbered year and ending June 30 of the following even-numbered year. Appointed members of the board are not required to be qualified electors nor residents of the district.
D. Appointed board members are authorized to vote on all matters except for a tax or assessment of any kind proposed or approved pursuant to authority granted by Article 8, § 9 of the constitution of New Mexico, which is limited to a vote of the elected members only.