N.M. Stat. § 73-9-10
[Location of office; secretary; notice of elections; election
board.]
The office of the board of directors shall be located in the county where the
organization was effected. Fifteen days before any election held under this act,
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 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 the
place in the precinct where the election must be held.