(B) The court of common pleas shall annually submit a written request for an appropriation to the board of county commissioners that shall set forth estimated administrative expenses of the court that the court considers reasonably necessary for its operation. The board shall conduct a public hearing with respect to the written request submitted by the court and shall appropriate the amount of money each year that it determines, after conducting the public hearing and considering the written request of the court, is reasonably necessary to meet all administrative expenses of the court.
If the court considers the appropriation made by the board pursuant to this division insufficient to meet all the administrative expenses of the court, it shall commence an action under Chapter 2731. of the Revised Code in the court of appeals for the judicial district for a determination of the duty of the board of county commissioners to appropriate the amount of money in dispute. The court of appeals shall give priority to the action filed by the court of common pleas over all cases pending on its docket. The burden shall be on the court of common pleas to prove that the appropriation requested is reasonably necessary to meet all its administrative expenses. If, prior to the filing of an action under Chapter 2731. of the Revised Code or during the pendency of the action, any judge of the court exercises the contempt power of the court of common pleas in order to obtain the amount of money in dispute, the judge shall not order the imprisonment of any member of the board of county commissioners notwithstanding sections 2705.02 to 2705.06 of the Revised Code.