Ohio Rev. Code Ann. § 2743.20

Appeals from orders and judgments of the court of claims lie to the same courts under the same circumstances, as appeals from the court of common pleas of Franklin county, and the same rules of law govern their determination. The decision of the court of claims with respect to an appeal from a decision of the the attorney general pursuant to sections 2743.51 to 2743.72 of the Revised Code is final, and no appeal from the decision of the court of claims lies to any other court.