In all causes appealed, or in any other manner brought from any inferior court to any superior court, the party appealing, or so bringing said suit into the superior court, may, in like manner, dismiss his appeal in the same manner as in the preceding section provided; and when said cause is dismissed, as aforesaid, the judgment in the inferior court shall remain and be in all things as valid, as if said cause had never been removed from said inferior court.
NMS § 39-3-14