§ 10-6-4 NMSA 1978

The officer, agent, employee, board or other agency of the state, or of its departments, agencies, counties, municipalities or political subdivisions, who is by law authorized to fill ordinary vacancies in the public office or employment so permanently abandoned, as provided in Section 3 [ 10-6-3 NMSA 1978] hereof, is hereby authorized, empowered and directed to appoint to such public office or employment some qualified person who shall thereafter receive the salary and perform the duties thereof until the expiration of the term of the former incumbent or until his successor shall have been elected, appointed or otherwise chosen and qualified or until the former incumbent shall have been relieved from active duty in the armed services and shall have resumed the personal discharge of the duties of such public office or employment.