N.M. Stat. § 73-13-4
Upon the application of any landowner in the district or upon its own motion, the board of directors of any such district may transfer any water rights appurtenant to lands held by or within such district, which for any cause are not suitable for irrigation or capable of being properly irrigated, to any other lands held by or within such district and which, in their judgment may be profitably and advantageously irrigated. Said action shall be taken by first publishing a notice in any newspaper published within the county where the office of said district is located, of the board's intention to consider a resolution setting a time and place thereof, which resolution shall have for its purpose the transfer of such water rights from certain lands described in said notice to certain other lands described in said notice, and the reason for such transfer. At such time and place protest or protests from any person or persons interested may be heard and thereafter said board of directors shall take formal action upon said resolution. Any protestant or protestants may appeal direct to the district court from any action taken by said board upon said resolution, provided said appeal be taken and notice thereof served within ten (10) days from the date of the adoption or rejection of such resolution.
Such appeal when so taken to the district court, shall be heard de novo and in all matters the same as appeals from justice of the peace courts [magistrate courts], except that no right of trial by jury shall be allowed.
NMS § 73-13-4