N.M. Stat. § 1-12-20
Conduct of election; interposing challenges.
A challenge may be interposed by a member of the precinct board [election board] or by a
party challenger for the following reasons:
A. the person offering to vote is not registered to vote;
B. the person offering to vote is listed among those persons to whom an absentee ballot
was mailed;
C. the person offering to vote has already cast a ballot in that election;
D. the person offering to vote is improperly registered because the person is not a qualified
elector; or
E. in the case of a primary election, the person desiring to vote is currently affiliated with a
major political party or a political party not represented on the ballot and the person requests a
ballot for a party with which the person is not affiliated.