No permit is or can be required. This state has a preemption clause which disallows any government other than the state to make firearm rules. makes carrying a lot easier as you travel through NM.
I have been a resident of NM for years and have owned and purchased a few guns over the years. I only Oc'd once here in Otero county. The one time I did I happened to be dropping off movies at our local blockbuster, which happened to get ran into by a ford explorer and the place was filled with local PD. I dropped off my movies with my 9mm on my hip in it's holster. They didn't say anything as I put the movies in the return box, but on my trip back to the car, they asked me if I had a permit to carry. I told them no, this state doesn't require a permit to OC. He told me he believed the city however does and that I shouldn't OC until I have one. I quickly left and haven't OC'ed since. I called the local PD here and they couldn't confirm a permit was needed. I called city hall and they told me to call the local PD. Does anyone actually know if a LTCF is needed in the city of Alamogordo?
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.)