N.M. Stat. § 1-10-7
Ballots; name shall appear but once; exceptions.
A. In a primary or general election, no candidate's name shall appear more than once on the
ballot, except in the case of a candidate who is also a candidate for president or vice president
of the United States.
B. In a regular local election, a candidate's name:
(1)
shall not appear more than once to be elected to any position with the same local
government; and
(2)
may appear more than once to be elected to any position with different local
governments.