N.M. Stat. § 73-18-34
Becoming a candidate for director.
Any person wishing to become a candidate for the office of director in any district
shall by the last Friday of July before the election file in the office of the secretary of the
district a declaration of candidacy stating the election precinct for which the person is a
candidate, accompanied by a petition signed by not less than ten qualified electors of
the election precinct for which the person is a candidate to represent. No declaration of
candidacy shall be accepted by the secretary unless accompanied by such petition,
signed by electors.