Even if not illegal, most folks would have some trouble finding a proper place for their captive critter. There are alternatives though. I live in the Tucson area of Arizona and have twice (so far) captured poisonous snakes: the first a coral snake which was far smaller than I would have thought and almost dainty. The second was a rattlesnake. Not dainty at all.. Both times I called 9-1-1 and the local fire department came out to relieve me of them. I asked, and they assured me that the snakes would be released in a safe, non-populated location. I wouldn't treat rats as kindly, but perhaps other animals, caught by ordinary citizens, could also be relocated by game wardens, etc.