If the respondent is not the prevailing party, the court may assess against the respondent all direct expenses and costs incurred by the prosecutor or other appropriate public official and law enforcement officers under section 3127.45 or 3127.46 of the Revised Code.
Assessment of enforcement expenses and costs against losing party
Ohio Rev. Code Ann. § 3127.47, under Chapter 3127 | Uniform Child Custody Jurisdiction And Enforcement Act.
Ohio Rev. Code Ann. § 3127.47