N.M. Stat. § 4-41-5
Deputy sheriffs; appointment and term; merit system.
The sheriffs in all the counties of this state shall have power to appoint deputies,
who shall remain in office at the pleasure of such sheriffs; except that in counties which
have established a merit system by ordinance, the provisions of the ordinance shall
control the demotion and discharge of deputies and other employees of the sheriff's
office, except for one under-sheriff and an executive secretary, both of whom shall hold
exempt positions.