If you're referring to a scenario where you are using the same exit node as someone doing illegal activity is using, no. You'd be safe, because an adversary watching the exit node's traffic would only know what was sent from the exit node, not who sent it. So long as you're not de-anonymizing yourself, (Ex. logging into sites associated with you, using a credit card which is in your name, etc.) you'd be fine.
If you're referring to a scenario where you're running a Tor exit node, and someone did something illegal from it, that depends on the laws of where you live. However, Tor exit nodes shouldn't be run from your home, and they should clearly identify themselves as Tor exit nodes. (take a look at a Tor blog post about exit nodes for some more information on that)