Scamp:
The "standard" repository for information along those lines is
www.packing.org, you should be able to find what you are looking for there.
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Added:
Ok, I did a little digging, and came up with this:
30-7-2. Unlawful carrying of a deadly weapon.
A. Unlawful carrying of a deadly weapon consists of carrying a concealed loaded firearm or any other type of deadly weapon anywhere, except in the following cases:
(1) in the person's residence or on real property belonging to him as owner, lessee, tenant or licensee;
(2) in a private automobile or other private means of conveyance, for lawful protection of the person's or another's person or property;
(3) by a peace officer in accordance with the policies of his law enforcement agency who is certified pursuant to the Law Enforcement Training Act [29-7-1 NMSA 1978];
(4) by a peace officer in accordance with the policies of his law enforcement agency who is employed on a temporary basis by that agency and who has successfully completed a course of firearms instruction prescribed by the New Mexico law enforcement academy or provided by a certified firearms instructor who is employed on a permanent basis by a law enforcement agency; or
(5) by a person in possession of a valid concealed handgun license issued to him by the department of public safety pursuant to the provisions of the Concealed Handgun Carry Act [29-19-1 NMSA 1978].
B. Nothing in this section shall be construed to prevent the carrying of any unloaded firearm.
C. Whoever commits unlawful carrying of a deadly weapon is guilty of a petty misdemeanor.
Which seems much more sensible than what we have here in Ga, where there is no open carry save for a few exceptions like hunting and the shooting range.
Oh, BTW -- there are some restrictions on where you can't carry, I haven't listed them. You might want to check out the relevant NM statutes
here, where I came up with that above info.