N.M. Stat. § 73-10-40
The board of directors, if they deem it not for the best interest of the district that the lands mentioned in the petition or some portion thereof, should be excluded from said district, shall order that said petition be denied; but if they deem it for the best interest of the district that the lands mentioned in the petition, or some portion thereof, be excluded from the district, and if there are no outstanding bonds of the district, then the board may order the lands mentioned in the pettiion [petition], or some defined portion thereof, to be excluded from the district; 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 exclusion of such lands from said district, said order shall be held for naught and such lands shall not be excluded therefrom.
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 shall be filed with the board of directors.
NMS § 73-10-40