N.M. Stat. § 72-12-15
No person owning or controlling lands shall permit the drilling of a well thereon for water from an underground source, as herein defined, by any person other than a driller licensed under the provisions of this act [72-12-12 to 72-12-17 NMSA 1978]. No person shall produce water from an underground source through any well drilled in violation of this act. No person shall apply water from such underground source to land having no valid water right for the purpose to which applied. The state engineer may apply for and obtain an injunction, in the district court of the county in which any well or land affected is situated, against any person, firm or corporation who shall drill or begin the drilling of a well in violation of the provisions of this act, or who shall cause, allow or permit the drilling of a well by a person other than a licensed driller upon land owned or controlled by him, or who shall produce water from any well drilled in violation of this act, or who shall apply water from an underground source, as hereinabove defined, to lands having no valid water right for the purpose to which applied. This provision shall in no wise be construed to affect the existing right of a court of equity in the exercise of its general equity powers to grant relief to the state of New Mexico by injunction or otherwise.
NMS § 72-12-15