N.M. Stat. § 73-12-8
The office of the board of directors shall be located in the county where the organization was effected. Fifteen (15) days before any election held under this act [73-12-1 to 73-12-57 NMSA 1978], subsequent to the organization of the district, the secretary who shall be appointed by the board of directors shall cause notice, specifying the polling places of each precinct, to be posted in three public places in each election precinct, of the time and place of holding the election, and shall also post a general notice of the same in the office of said board, which shall be established and kept at some fixed place to be determined by said board in said county. Prior to the time for posting the notices, said board must appoint from each precinct, from the electors thereof, three judges, one of whom shall act as clerk, who shall constitute a board of election for such precinct. If the board fails to appoint a board of election, or the members appointed do not attend the opening of the polls on the morning of the election, the electors of the precinct present at the hour may appoint the board or supply the place of an absent member thereof. The board of directors must, in its order appointing the board of election, designate the hour and place in the precinct where the election must be held.
NMS § 73-12-8