No. Only a home that tests high needs one: the EPA recommends fixing at 4 pCi/L or above and considering it between 2 and 4. But every home should be tested, because two houses on the same Central Ohio street can read very differently.
More detail
The Ohio Department of Health recommends testing every occupied building that touches the ground, and the EPA says its zone map should not be used to decide whether a particular house needs a test. For a home that is not being sold, Ohio's recommended sequence starts with one short-term test in the lowest livable level. Under 4 pCi/L, no action beyond a retest in two years or after renovations. Between 4 and 8, a second short-term test or a long-term test sharpens the picture. At 8 or higher, a second short-term test, then a decision on the average. Some households choose to fix results between 2 and 4, especially when someone smokes or sleeps on the lowest level. See what your number means.