Ohio Rev. Code Ann. § 6117.18

The probate judge shall make a record of all proceedings before him, and tax the cost in favor of the prevailing party and against the losing party. If more than one matter is appealed from, and a party prevails as to one matter and loses as to another, the probate court shall determine how much of the costs each party shall pay. The costs on motions or continuance and the like shall be taxed and paid as the court directs. If there are several persons upon the side taxed with costs the court shall apportion the costs equitably among them, and in case several persons are interested on one side of the case and part of them fail, the court shall make such order as to costs as it deems equitable. In cases not specifically provided for, the court shall render such judgment in respect to costs as is equitable. The board of county commissioners shall pay any costs adjudged against it out of the county treasury.