This is released on 1998 on Quest for Camelot
The title makes reference to the novel 'The Strange Case of Dr Jekyll and Mr Hyde' by Robert Louis Stevenson. One of several uses of this story by the Warner Brothers animation department.
WB generally characterized Dr. Jekyll as a meek and mild older gent, unlike his portrayal in films.
Sylvester breaks the fourth wall when he asks the audience if he has a choice whether to jump or not.
The opening credits cleverly illustrate what the people listed actually do (music, animation, etc).