No Ohio rule assigns it. It gets negotiated: the seller installs a system before closing, the seller gives a credit, or the buyer takes it on. Get a written scope before the inspection response deadline so the number on the table is real.
More detail
A system installed before closing, with the post-mitigation result in hand, is usually the cleanest outcome for a buyer, because Ohio's standards then hand over a closeout package, a floor plan, and a license number to call. A credit works when time is short, but it should be sized from a written proposal rather than a guess; a crawl space or a second suction point can move the price from the $1,200 to $2,400 range into the $1,800 to $3,500 tier. If the seller installs, the buyer can ask for the post-mitigation test to be run by an independent Ohio-licensed tester, which the rules allow. Sellers can skip the scramble entirely by testing before listing. See the real estate radon service.