N.M. Stat. § 72-5-3
The date of receipt of such formal application in the state engineer's office shall be endorsed thereon and noted in his record. If the application is defective as to form, or unsatisfactory as to feasibility or safety of plan, or as to the showing of ability of the applicant to carry the construction to completion, it shall be returned with a statement of the corrections, amendments or changes required, within thirty days after its receipt, and sixty days shall be allowed for the refiling thereof. If refiled, corrected as required within such time, the application shall, upon being accepted, take priority as of date of its original filing, subject to compliance with the further provisions of the law and the regulations thereunder. Any corrected application filed after the time allowed [shall] be treated in all respects, except as to filing fees, as an original application received on the date of its refiling; provided, that the plans of the construction may be amended at any time upon the approval of the state engineer, except that a change in the proposed point of diversion of water from a stream or watercourse shall be subject to the provisions of Section 72-5-24 NMSA 1978 as amended and the rules and regulations of the state engineer.
NMS § 72-5-3