(a) Any party, either relator or defendant, in any habeas corpus case shall have the right of appeal to the proper appellate court from any judgment or decree rendered against such party by an inferior court.
(b) The party so appealing shall give bond and security for the costs of such appeal except where the relator or defendant is under confinement and serving a prison sentence on final judgment.
(c) This section shall not apply to parties held in custody in criminal cases.