Brook lands in prison due to some illegal political activism. In a flashback during season four, we learn that she used to be a door-to-door activist. One day, she agrees to go to the house of a registered sex offender if a guy she has a crush on will go out with her. She goes, and it turns out that he's actually a really nice guy who got a bad rap. Once she gets back to headquarters, she boasts about how awful he was and that he tried to seduce her. That's as far as we've gotten into Brook's backstory, but I'm betting that she takes her lie too far and the guy presses charges for further besmirching his already tainted name.