You have the right to do inspections and any testing you would like on any property you purchase in Wisconsin. However on an ROE property the bank may not be willing to do any repairs. You should never buy a property you have not done an inspection on. The buyer pays for any test and inspection except for well and septic. All REO properties are listed as is in Wisconsin. You would have to write in an offer that you want an inspection and list any testing that you would want. This can not be done after the offer is excepted. This is an inspection contingency.
Most states do not require REO owners to make any discloures such as Radon, other NHD issues, death on the property, property condition, etc. If you are concerned about Radon, have your agent order an NHD with Environmentals, Radon, & CLUE. It should only cost about $150. but could be well worth it if you're concerned to put your mind at ease, or to back out.