Ohio does not require landlords to test rental housing for radon. Once you know of an elevated result, the calculus changes, because a known hazard you did not address is a different position than one you never measured.
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There is no Ohio statute requiring a landlord to test a residential rental for radon before leasing, and no general obligation to provide a result a tenant has not asked for. Some states have testing or disclosure requirements for rentals; Ohio is not currently one of them. That is the legal floor rather than the practical answer. Two things shift the analysis. The first is knowledge: once a test has been run and shows an elevated result, an owner is in possession of information about a known health hazard in a unit they are renting out, and doing nothing with it is a materially different position than never having measured. The second is that tenants increasingly ask, particularly in a region where elevated results are common, and an owner who can answer the question with a documented result and a system has an easier conversation than one who cannot. For multi-unit buildings the technical picture also changes. Ground-contact units carry the exposure, upper floors generally do not, and shared HVAC or stairwells can move soil gas between units in ways single-family testing does not account for. Buildings large enough to fall under ANSI/AARST CC-1000 for large-building mitigation need a different scope than a house. The pragmatic position most owners land on: test the ground-contact units, keep the results, and mitigate what comes back high. A system costs roughly one month of rent in this market and it removes the question permanently.