N.M. Stat. § 73-14-61
Any qualified elector who desires to become a candidate for election as a director shall file with the proper filing officer in accordance with the provisions of the Local Election Act [Chapter 1, Article 22 NMSA 1978] a written notice of candidacy, which shall state the candidate's name and residence within the conservancy district. If the candidate is a candidate at large, the candidate's notice of candidacy shall be signed by twenty qualified electors resident within the district. If the candidate is a candidate only from that portion of the district that lies within one county, the candidate's notice of candidacy shall be signed by ten qualified electors who reside within that particular portion of the district and county from which the candidate seeks to be elected.
NMS § 73-14-61