Ohio Rev. Code § 2731.11: Recovery of damages.

If judgment in a proceeding for a writ of mandamus is rendered for the plaintiff, the relator may recover the damages which he has sustained, to be ascertained by the court or a jury, or by a referee or master, as in a civil action, and costs. A peremptory mandamus shall also be granted to him without delay.

Such recovery of damages against a defendant is a bar to any other action upon such cause of action.