(a) All persons having demands against any county shall present them, duly verified according to law, to the county court of the county for allowance or rejection.
(b) From the order of the court thereon, appeals may be prosecuted as provided by law. If on any such appeal the judgment of the county court is reversed, the judgment of reversal shall be certified by the court rendering it to the county court, and the court shall thereupon enter the judgment of the superior court as its own.