Ohio Rev. Code Ann. § 5901.37

In any county having a cemetery or part of it set apart for the burial of veterans, or containing a monument erected to their memory, or containing monuments and memorials erected by private or public expense to the memory of veterans, the board of county commissioners shall care for and properly preserve that portion of the cemetery so set apart for the burial of such veterans, and shall care for and properly preserve the monuments or memorials, and the board shall pay all expenses incident to such care and preservation from the general fund of the county.