Well, how we do it at my school is we have a cast that knows a basic storyline and base of events that goes on, but everything else is fully improve as their characters. Then mini skits go on and there are times that the audience can go around to the cast and ask questions and such, which they answer in character. And then there is a time where they need the help of the audience to figure out who it is, and they vote who they think the killer(s) are. And depending how many people got it right, they usually go into a drawing and get drawn for the prizes.
It's really fun, and gets a lot of good reviews. I think doing it that way might be the best, so you don't have to totally mess with the audience but they still get to partisipate a bit.