Ohio Rev. Code Ann. § 3119.302
(A) When the court, with respect to a court child support order, or the child support enforcement agency, with respect to an administrative child support order, determines the person or persons responsible for the health care coverage of the children subject to the order pursuant to section 3119.30 of the Revised Code, all of the following apply:
(2) If the cost of health insurance coverage to either parent exceeds a reasonable cost, that parent shall not be ordered to provide health insurance coverage for the child except as follows:
(4) Notwithstanding division (B) of section 3119.29 of the Revised Code, the court or agency may do either of the following: