N.M. Const. art. V, § 5

[Governor's appointive and removal power; interim appointees.] The governor shall nominate and, by and with the consent of the senate, appoint all officers whose appointment or election is not otherwise provided for and may remove any officer appointed by him unless otherwise provided by law. Should a vacancy occur in any state office, except lieutenant governor and member of the legislature, the governor shall fill such office by appointment, and such appointee shall hold office until the next general election, when his successor shall be chosen for the unexpired term. (As amended November 8, 1988.)