N.M. Stat. § 77-1A-5

A. An animal control authority shall issue a certificate of registration to the owner of a potentially dangerous dog if the owner establishes that:

(1) the owner is able to keep the dog under control at all times;

(2) a license, if applicable, has been issued pursuant to the requirements of the jurisdiction;

(3) the dog has a current rabies vaccination;

(4) the owner has a proper enclosure for the dog;

(5) the owner has paid an annual fee, if applicable, established by the animal control authority to register a potentially dangerous dog;

(6) the dog has been spayed or neutered;

(7) the dog has been implanted with a microchip containing owner identification information that is also provided to the animal control authority; and

(8) the owner has entered the dog in a socialization and behavior program approved or offered by the animal control authority.

B. If a dog previously determined to be potentially dangerous has not exhibited any of the behaviors specified in Subsection D of Section 2 1 of the Dangerous Dog Act for thirty-six consecutive months, the owner may request the animal control authority in the jurisdiction to lift the requirements for registration pursuant to this section. If the animal control authority has no reasonable basis to believe that the dog has exhibited the behaviors specified, it shall relieve the owner of the requirements of this section.

C. An animal control authority shall issue a certificate of registration to the owner of a dangerous dog if the owner, in addition to the requirements of Subsection A of this section, establishes that:

(1) the owner has paid an annual fee, if applicable, established by the animal control authority to register a dangerous dog;

(2) the owner has written permission of the property owner or homeowner's association where the dangerous dog will be kept, if applicable;

(3) the dangerous dog will be maintained exclusively on the owner's property except for medical treatment or examination;

(4) when the dangerous dog is removed from the owner's property, the dog shall be caged or muzzled and restrained with a lead no longer than four feet, and the dog shall be under complete control at all times;

(5) the dangerous dog will not be transported in a vehicle that might allow the dog to escape or gain access to any person or animal outside the vehicle; and

(6) a clearly visible warning sign with a conspicuous warning symbol indicating that there is a dangerous dog on the premises is posted where the dog is kept and is visible from a public roadway or from fifty feet, whichever is less.

D. An animal control authority may order the immediate impoundment or humane destruction of a dog previously determined to be a dangerous dog if the owner fails to abide by the conditions for registration, confinement or handling set forth in this section.