Ohio Rev. Code § 5505.29
The state highway patrol retirement board shall refund the cost of service credit restored under section 5505.20 or purchased under division (D) of section 5505.16, division (C) of section 5505.17, or section 5505.201, 5505.25, 5505.40, or 5505.402 of the Revised Code to the extent the credit does not, or, in the case of a person who retired or died prior to June 30, 2000, did not, increase the pension provided to the retirant or surviving spouse under section 5505.16, 5505.162, 5505.17, or 5505.18 of the Revised Code. The board shall provide the refund to the retirant or surviving spouse or, if there is no surviving spouse, the beneficiary designated by the retirant on a form provided by the state highway patrol retirement system. A retirant may designate an individual or a trust as a beneficiary. If there is no surviving spouse or designated beneficiary, the refund shall be provided to the retirant's estate. The refund cancels an equivalent amount of service credit.
R.C. § 5505.29