N.M. Stat. § 72-2-16
The state engineer may order that a hearing be held before the state engineer enters a decision, acts or refuses to act. If, without holding a hearing, the state engineer enters a decision, acts or refuses to act, any person aggrieved by the decision, act or refusal to act is entitled to a hearing if a request for a hearing is made in writing within thirty days after receipt by certified mail of notice of the decision, act or refusal to act. Hearings shall be held before the state engineer or the state engineer's appointed examiner. Hearings shall be held in the county in which the water right at issue is adjudicated, licensed or permitted, unless the parties and the state engineer stipulate another site for the hearing. A record shall be made of all hearings. An appeal shall not be taken to the district court until the state engineer has held a hearing and entered a decision in the hearing.
NMS § 72-2-16