N.M. Stat. § 1-4-15
Registration; change of party affiliation.
A. A voter may change the voter's designated party affiliation by executing a new certificate
of registration indicating the change of party affiliation.
B. A voter who has previously declined to designate a party affiliation on the voter's
certificate of registration but who desires to designate a party affiliation on the voter's certificate
of registration shall execute a new certificate of registration indicating the desired party
affiliation.
C. A voter who does not designate on the certificate of registration a party affiliation shall be
considered to have declined to designate a party affiliation.
D. A voter who has declined to designate on the voter's certificate of registration a party
affiliation but who chooses to affiliate with a major political party that is participating in a primary
election may do so by requesting the ballot of one of the parties participating in that primary
election. The voter's certificate of registration shall not be changed to reflect a new or different
party affiliation unless the voter so requests in accordance with the provisions of Subsection B
of this section.