N.M. Stat. § 10-6-3
Any incumbent of any public office or employment of the state of New Mexico, or of any of its departments, agencies, counties, municipalities or political subdivisions whatsoever, who shall accept any public office or employment, whether within or without the state, other than service in the armed forces of the United States of America, for which a salary or compensation is authorized, or who shall accept private employment for compensation and who by reason of such other public office or employment or private employment shall fail for a period of thirty successive days or more to devote his time to the usual and normal extent during ordinary working hours to the performance of the duties of such public office and employment, shall be deemed to have resigned from and to have permanently abandoned his public office and employment.
NMS § 10-6-3