New Mexico Territorial Laws and Treaties NM TERR LAWS KEARNY CODE CT & J POWERS § 43

Appeals shall be allowed from judgments of alcaldes when the debt or damages do not exceed fifty dollars, to the prefect, in all other cases to the circuit court, in the same manner, and subject to the same restrictions as in cases of appeals from the circuit to the supreme court; provided that an appeal may be taken from the judgment of an alcalde within ten days of the rendition of the judgment.