-The only place in New Mexico that has an ordinance prohibiting keeping bees is within Alamagordo city limits.  

-All other locations in New Mexico follow the NM Bee Rule

Here are the highlights of the NM Bee Rule

A "commercial apiary" means any location or single beeyard North of I-40 where 15 or more colonies are located or South of I-40 where 25 or more colonies are located

If you qualify as a "commercial apiary" you have to register your apiary and pay an annual registration fee that runs $3 per apiary per year. This amount can be paid through Greg Watson, Assistant Bureau Chief, NM Dept of Agriculture, NMDA inspector for NM. He can be contacted at gwatson@nmda.nmsu.edu or (505) 646-3207

If you are a "commercial apiary" you need to obtain a pollination permit to move bees for pollination purposes within 1 1/2 miles of another beekeeper's registered apiary. 

On a side note. The NM Bee Rule came about to keep competitive commercial beekeepers from putting yards too close to each other and getting into beeyard wars. If you want to keep bees, there is nothing stopping you besides remembering that the nectar sources in NM are scarce and we shouldn't try and put pressure on the nectar reserves of existing nearby beekeepers.