New Mexico Territorial Laws and Treaties NM TERR LAWS KEARNY CODE ELEC § 32

If the person whose seat is contested fail to select an alcalde, as provided for in the next preceding section, the person contesting the same shall proceed to select another alcalde, without delay, and the two alcaldes thus selected by the contestor shall, in such event, have full power and authority to take depositions of witnesses who may be brought before them to be examined.