Is it possible that there was a nest in the attic? If so, the squirrel will try to chew its way back in to get to the young. You will need a permit to trap the squirrel. The permit is free. The squirrel would have to be released back onto the same property unless you have permission from the landowner of another property to release the squirrel there. It is illegal to release wildlife into parks, natural areas, forest preserves, etc.
The Illinois Department of Natural Resources district wildlife biologists are the ones who issue the permits. Depending on whether you live in Cook or Will County, you'll need to contact: Cook Co.: Bob Massey at (815) 476-0256 Will Co.: Joe Rogus at (815) 476-2523 Please let me know if you have more questions.