N.M. Admin. Code § 7.4.2.10
Any district health officer may declare a quarantine against rabies within the health district or any part thereof when rabies has been determined to exist to the extent that it is a danger to public health. Upon written findings of such danger and approval of the division director of the public health division, all animals designated in the quarantine order and living within the area specified in the order shall be confined as directed by the district health officer. Any reasonable effort to apprehend any dog or cat running at large and uncontrolled by its owner during a period of quarantine, any animal control officer or peace officer may destroy the dog or cat and properly dispose of the body. The district health officer may order other measures as may be necessary to prevent the spread of rabies. A quarantine shall not be removed except by order of the district health officer.
N.M. Admin. Code § 7.4.2.10