Ohio Rev. Code § 2151.19: Summons - expense.

The summons, warrants, citations, subpoenas, and other writs of the juvenile court may issue to a probation officer of any such court or to the sheriff of any county or any marshal, constable, or police officer, and the provisions of law relating to the subpoenaing of witnesses in other cases shall apply in so far as they are applicable.

When a summons, warrant, citation, subpoena, or other writ is issued to any such officer, other than a probation officer, the expense in serving the same shall be paid by the county, township, or municipal corporation in the manner prescribed for the payment of sheriffs, deputies, assistants, and other employees.