New Mexico Territorial Laws and Treaties NM TERR LAWS KEARNY CODE ELEC § 30

If any candidate of the proper county or district contest the election of any person proclaimed duly elected by either house of the general assembly, such person shall give notice in writing to the person whose election he contests, or leave a written notice thereof at the house where such person last resided, within forty days after the return of the election to the clerk's office; the notice shall specify the names of the voters whose votes are contested, the grounds on which such votes were illegal and the name of the alcalde who will attend to taking of the depositions, and where he will attend to take the same.