Here is the website of the State Engineer, who handles this. https://www.ose.nm.gov/WR/WRindex.php - This is supposed to be legal, but you need to use a registered driller. I found no local ordinance prohibiting a domestic well, but there may be some reason there aren't any that I can see. However, I don't see wells in the county either, so that may not mean much.

This is a good site for this (but work blocks pop-ups): http://nmwrrs.ose.state.nm.us/nmwrrs/waterColumn.html

Here is the GIS for NM Water Pods - https://gis.ose.state.nm.us/gisapps/ose_pod_locations/