N.M. Stat. § 1-12-7
Conduct of election; persons not permitted to vote; persons
permitted to vote upon choosing to affiliate with a party.
A. A person shall not vote in a primary, general or statewide special election unless the
person is a voter of the county in which the person offers to vote. A valid original certificate of
registration in the county register is prima facie evidence of being a voter in the precinct.
B. A person at a primary election shall not be permitted to vote for the candidate of any
party other than the party designated on the person's current certificate of registration; provided
that a person who has declined to designate a political party affiliation on the person's certificate
of registration shall be permitted to choose to affiliate with a major political party in a primary
election by requesting a major political party's primary election ballot and shall be permitted to
vote for the candidates on that party's ballot.