N.M. Stat. § 73-10-31
The board of directors if they deem it not for the best interests of the district to include therein the lands mentioned in the petition, shall by order reject the said petition, but if they deem it for the best interests of the district that said lands be included the board may order that the district be so changed as to include therein the lands mentioned in the said petition. The order shall describe the entire boundaries of the district with the lands so included, if the district boundaries be changed thereby, and for that purpose the board may cause a survey to be made of such portion of such boundaries as may be deemed necessary; provided, if within thirty days from the making of such order a majority of the qualified electors of the district protest in writing to said board against the inclusion of such lands in said district, said order shall be held for naught and said lands shall not be included therein.
Provided, further, that in case contract has been made between the district and the United States as in Section 13 [73-10-16 NMSA 1978] hereof provided, no change shall be made in the boundaries of the district and the board of directors shall make no order changing the boundaries of the district until the secretary of the interior shall assent thereto in writing and such assent be filed with the board of directors.
NMS § 73-10-31