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When you are browsing regular WWW through Tor last node's (exit node's) IP is known to the server, also exit node's ISP can observe the traffic.
So if somebody is browsing sites with illegal content (for example child pornography) and you happen to be the last node doesn't it seem to authorities that you were doing this and not said person?
Yes, that is a distinct possibility.
To prevent this the Tor project recommends a range of actions to make it clear you're running an exit relay; for instance informing your ISP.
You can read a blog post regarding this here.
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)
