§ 1-4-7 NMSA 1978

A qualified elector who is temporarily out of his county of residence or out of New Mexico, may, upon request to the county clerk of his county of residence, obtain the prescribed certificate of registration form. After the certificate of registration has been subscribed, the qualified elector shall return it to the county clerk of his county of residence by mail. Upon receipt of the completed certificate of registration, the county clerk shall ascertain if such certificate of registration is to be filed or rejected in accordance with the Election Code [Chapter 1 NMSA 1978].