New Mexico Territorial Laws and Treaties NM TERR LAWS KEARNY CODE ELEC § 33

The person whose seat is contested, if he intends to contest the legality of any votes given to the candidate who contests the same, shall, within twenty days after he is notified that his election will be contested, give to the adverse party a similar notice to that specified in the thirtieth section of this law, and the candidate to whom the notice is given shall proceed to select an alcalde in the same manner as is provided for in the thirty-first section, and on his failing to do so the party giving the notice shall, without delay, select another alcalde, and the two alcaldes so selected, by the party proclaimed duly elected, shall proceed to take the depositions of such witnesses as may be brought before them to be examined; provided, however, that either party may, without notice, take rebutting testimony before the alcaldes at the time and place specified for taking depositions.