The title is a play on the expression "neither hide nor hair."
Bugs comes out of his rabbit hole in a city park every morning because a kind gentleman (who has the likeness and mannerism of Peter Lorre) keeps coming to feed him a carrot ("Well, here I go again with the 'timid little rabbit' routine. It's shameful, but- eh, it's a living!"). At first feigning a usual rabbit posture, Bugs eventually stands up and confides that he'd rather simply go home with the gentleman as a "pet", since it would be easier on both of them. As the gentleman brings Bugs home, he remarks that it is strange that Bugs calls him "Doc" because "I happen to be a doctor." The camera then pans up to see that the name above the apartment is none other than Dr. Jekyll.