New Mexico Statutes Chapter 3. Municipalities § 3-18-3. Animals

(1) prohibit cruelty to animals;

(2) regulate, restrain and prohibit the running at large of any animal within the boundary of the municipality; and

(3) provide by ordinance for the impounding and disposition of animals found running at large. Prior to the time set for disposing of the animal as provided in the ordinance, the owner may regain possession of the animal by paying the poundmaster all costs incurred in connection with impounding the animal.