N.M. Stat. § 72-5-23
All water used in this state for irrigation purposes, except as otherwise provided in this article, shall be considered appurtenant to the land upon which it is used, and the right to use it upon the land shall never be severed from the land without the consent of the owner of the land, but, by and with the consent of the owner of the land, all or any part of the right may be severed from the land, simultaneously transferred and become appurtenant to other land, or may be transferred for other purposes, without losing priority of right theretofore established, if such changes can be made without detriment to existing water rights and are not contrary to conservation of water within the state and not detrimental to the public welfare of the state, on the approval of an application of the owner by the state engineer. Publication of notice of application, opportunity for the filing of objections or protests and a hearing on the application shall be provided as required by Sections72-5-4 and 72-5-5 NMSA 1978.
NMS § 72-5-23