Copyright laws for caricature of television/movie character?

I'm a caricature artist trying to create some work for a local art show. I've checked up on copyright laws regarding celebrity caricatures and found that there's some leeway there for "fine art" of modified celebrity likeness, but what about caricatures of celebrities drawn as a specific character they portray? For example, I'd like to draw Hugh Laurie as his role in House MD. Would I be breaking other copyright laws by involving the show, or would it be the same as if I drew him outside of the context of his role?