Hi, I'm thinking about run a relay on my computer but what is my responsibility when somebody do some various bad things at the internet? If somebody did something, would I be treat as climinal?

I suppose you've read this:
http://www.torproject.org/eff/tor-legal-faq.html.en

IANAL, and probably LQ's not the best place to seek legal advice... which probably tremendously differs depending on where you live.

I know nothing about Polish law. However, I would point out that even if you are not criminally responsible for illegal actions done using Tor from your computer, that doesn't protect you from police investigation. Your life can be ruined even if your are, and are found by the court to be, innocent. Just imagine your name and face splashed across the newspapers with a story about you being charged with downloading/uploading child porn.

You would also need to make sure that your computer was squeaky-clean, since having arrested someone, law enforcement often gets a "we'll get him for something mentality", so if they find for example pirate material they might charge you with that even though it's unrelated to what they came for.

I've heard nothing about accuse somebody for being tor relay in poland, but I will refrain from be relay. Thanks for replies.

If you want to help out the TOR network (thanks!) you don't need to be an end-point. You could set up the machine to be a middle node (or whatever it's in TOR-speak). So your machine could help out and not be visible outside of the TOR network.