Ohio Rev. Code Ann. § 2323.35

In an action in which security for costs has been given, at any time before commencement of the trial, after reasonable notice to the plaintiff, the defendant may move the court for additional security. On such motion if the court is satisfied that the surety has removed from this state, or is not sufficient, the action may be dismissed, unless, in a reasonable time, to be fixed by the court, sufficient security is given.