New Mexico does NOT have permitless (constitutional) concealed carry. Carrying a concealed loaded firearm in public is a petty misdemeanor unless the carrier holds a valid CHL issued under the Concealed Handgun Carry Act or qualifies for a statutory exception (own residence/property, private vehicle for lawful protection, peace officer). The state does allow permitless OPEN carry of a loaded firearm.
"A person in possession of a valid concealed handgun license issued by the department of public safety pursuant to the Concealed Handgun Carry Act shall be exempt from the provisions of this section."
NMSA 1978 § 30-7-2 (concealed loaded firearm requires CHL) secondary