Ohio Rev. Code § 5901.32
Upon securing the report and statement of expenses as provided by section 5901.27 of the Revised Code, the board of county commissioners shall transcribe in a book to be kept for that purpose, all the facts contained in the report concerning a deceased veteran, and shall certify the expenses thus incurred to the county auditor, who shall draw a warrant for those expenses upon the county treasurer, to be paid from the county fund to such persons as are designated by the board. Upon the death of any indigent veteran residing within the county at the time of death and the burial of the indigent veteran or the indigent veteran's cremated remains, the board shall make application to the proper authorities, under the United States government, for a suitable headstone, as provided by act of congress, and shall cause it to be placed at the grave of the deceased veteran or the deceased veteran's cremated remains.
R.C. § 5901.32