N.M. Stat. § 73-1-26
That any artesian conservancy district which has heretofore been organized, or may be hereafter organized, as provided by law, shall in addition to the powers granted to such districts have the right, power and authority to protest or object to any application made to the state engineer to appropriate any waters included within the boundaries of such conservancy district which may be subject to appropriation as provided by law, and to protest or object to any application to the state engineer to change the location of any well or to change the use of waters for any purpose other than that for which originally granted, where it is determined by resolution of the board of directors of such district that the granting of such proposed application would interfere with any existing water rights or program of such conservancy district for the conservation of the waters sought to be appropriated, and such district shall have the right to appeal to the district court from the decision of the state engineer within the time and manner provided by law for appeals from such decisions.
NMS § 73-1-26