New Mexico Statutes Chapter 1. Elections § 1-17-4. Referendum petitions;  penalty

A. sign any name other than his own, except to write thereon the name of a person who cannot write and who signs his name with his mark;

B. sign his name more than once on a petition on the same law;

C. sign his name when he is not a qualified elector in the county specified in the petition;  or

D. knowingly misrepresent the purpose and effect of the petition or law thereby affected, for the purpose of causing anyone to sign the petition in reliance upon such misrepresentation.