If this is for a rebellious teenager's shirt, You can't make me would probably be the most defiant (and still family-friendly) version of "I don't have to do anything."
Alternatively, you could expand the phrase to I don't have to do anything I don't want to do, but it seems a bit unwieldy for a shirt. (Maybe just saying I don't have to would be sufficient to get the idea across, but it might leave some passers-by wondering.)
You could also make it a bit more slang-ish with something like don't gotta do nothing (though note that this isn't technically a grammatically correct phrase, and probably wouldn't be said by an official).
(Note: American English)