The judge of probate shall examine said petition and also the tax books of his county; and, if the facts set forth in the petition are such as to entitle the petitioner to the refunding of the money as prayed for, he shall so certify to the Comptroller, stating the amount to be refunded by the state, and forward to the Comptroller a copy of the petition with his certificate endorsed thereon; and, if the Comptroller shall be satisfied that the petitioner is entitled to have the money refunded to him, he shall draw his warrant on the Treasurer in favor of the petitioner for such an amount as the certificate of the probate judge shows should be refunded.