"What you did is a crime."
Translation:To co zrobiłeś jest przestępstwem.
"zbrodnia" sounds very, very, very serious, like from "Crime and Punishment" (Zbrodnia i kara). But it's correct and accepted.
Wikipedia says that "In ordinary language, a crime is an unlawful act punishable by a state or other authority. The term crime does not, in modern criminal law, have any simple and universally accepted definition [...]" and it seems to me that even if in legal terms those can be different, "crime" should match "przestępstwo" in the way it's used in everyday language. "offence" is accepted when translating into English.