Article II Section 6 of The New Mexico Constituion is The New Mexico Preemption Law governing Firearms in New Mexico, and it reads:
Sec. 6. [Right to bear arms.]
No law shall abridge the right of the citizen to keep and bear arms for security and defense, for lawful hunting and recreational use and for other lawful purposes, but nothing herein shall be held to permit the carrying of concealed weapons. No municipality or county shall regulate, in any way, an incident of the right to keep and bear arms. (As amended November 2, 1971 and November 2, 1986.)
The underlineded part Preempts Local Governments from imposing Firearm Statutes any stricter than New Mexico Law governing that subject matter.