You actually want to call the Office of the State Engineer. They are the ones who deal with water rights and well drilling approval. You will be concerned with subsurface water from the Lower Rio Grande Basin, which is dealt with very differently than surface water (i.e. irrigation districts, interstate compacts, the river and its reservoirs). Water rights, in my experience, are usually attached to the property unless it spells out that they aren't. Of course you have to do your due diligence.
The fact that the adjudication of water rights (legally deciding once and for all who owns what) for the LRGB is ongoing further muddies the waters, so to speak.
All that aside there is no guarantee you will find water at an economically feasible depth. The lack of surface irrigation water in the Rio Grande Basin has led to widespread heavy pumping of subsurface water recently and many wells have gone dry. Do your homework.
New Mexico Office of the State Engineer / Interstate Stream Commission