N.M. Admin. Code § 19.25.13.23
Objections to any act or failure to act of a water master shall be made in the first instance informally, or in writing, to the water master who shall take prompt action on the objection if he determines that any action is warranted. If the water master fails to resolve the objection, further objections shall be made to the state engineer, who shall hear the matter in accordance with Section 72-3-3 NMSA. Streamlined processes for the prompt hearing of appeals from water master decisions shall be set up for each water master district. Filing of an objection to an act or failure to act by the water master will not stay the water master's action or failure to act, or his authority to administer the water right, pending resolution of the objection.
N.M. Admin. Code § 19.25.13.23