N.M. Stat. § 73-20-38
District supervisors; election and appointment; organized
districts.
A. Successors to supervisors whose terms end in a calendar year shall be elected
pursuant to the Local Election Act [Chapter 1, Article 22 NMSA 1978]. Elections shall be
called, conducted and canvassed in accordance with the Local Election Act.
B. By June 15 of each year, the district supervisors may submit to the commission a
list of persons interested in the district and who by experience or training are qualified to
serve as supervisors. The commission may appoint from the list submitted two persons
to serve as supervisors if it is the determination of the commission that the
appointments are necessary or desirable and would benefit or facilitate the work and
functions of the district. In the event a list is not submitted to the commission by the
supervisors by June 15, the commission may appoint two supervisors qualified to serve
by training or experience. Appointed supervisors shall serve a term of one year and
shall have the same powers and perform the same duties as elected supervisors.
Successors to appointed supervisors, or replacement-appointed supervisors in the
event of vacancy, shall be appointed by the commission from a list of candidates in
accordance with the provisions of this subsection.