David Huxley (Grant) is the stuffy paleontologist who needs to finish an exhibit on dinosaurs and thus land a $1 million grant for his museum. At a golf outing with his potential benefactors, Huxley is spotted by Susan Vance (Hepburn) who decides that she must have the reserved scientist at all costs. She uses her pet leopard, Baby, to trick him into driving to her Connecticut home, where a dog wanders into Huxley's room and steals the vital last bone that he needs to complete his project. The real trouble begins when another leopard escapes from the local zoo and Baby is mistaken for it, leading Huxley and Susan into a series of harebrained and increasingly more insane schemes to save the cat from the authorities. Inevitably, the two end up in the local jail, where things get even more out of hand: Susan pretends to be the gun moll to David's diabolical, supposedly wanted criminal.
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