David Huxley is a mild-mannered paleontologist. For the past four years, he has been trying to assemble the skeleton of a Brontosaurus but is missing one bone: the "intercostal clavicle." Adding to his stress is his impending marriage to Alice Swallow and the need to impress Elizabeth Random, who is considering a million-dollar donation to his museum.
The day before his wedding, David meets Susan Vance by chance on a golf course. She plays his ball, but refuses to accept that she has made a mistake. She is a free-spirited, somewhat scatterbrained, young lady, unfettered by logic. These qualities soon embroil David in several frustrating incidents.
Susan's brother Mark has sent her a tame leopard named Baby (Nissa) from Brazil. Its tameness is helped by hearing the song "I Can't Give You Anything But Love". Susan thinks David is a zoologist, and manipulates him into accompanying her in taking Baby to her farm in Connecticut. Complications arise when Susan falls in love with him, and she tries to keep him at her house as long as possible, even hiding his clothes, to prevent his imminent marriage.
David's prized intercostal clavicle is delivered, but Susan's aunt's dog George takes it and buries it somewhere. When Susan's aunt arrives, she discovers David in a negligee. To David's dismay, she turns out to be Elizabeth Random. A second message from Mark makes clear the leopard is for Elizabeth, as she always wanted one. Baby and George run off. The zoo is called to help capture Baby. Susan and David race to find Baby before the zoo and, mistaking a dangerous leopard (also portrayed by Nissa) from a nearby circus for Baby, they let it out of its cage.
David and Susan in jailDavid and Susan are jailed by a befuddled town policeman, Constable Slocum, for acting strangely at the house of Dr. Fritz Lehman, where they have cornered the circus leopard, thinking it is Baby. When Slocum does not believe their story, Susan tells him they are members of the "Leopard Gang"; she calls herself "Swingin' Door Susie," and David "Jerry the Nipper."[a] Eventually, Alexander Peabody shows up to verify everyone's identity. Susan, who escapes out of a window during a police interview, unwittingly drags the highly irritated circus leopard into the jail. David saves her, using a chair to shoo the big cat into a cell.
Some time later, Susan finds David, who has been jilted by Alice because of her, on a high platform working on his Brontosaurus reconstruction at the museum. After showing him the missing bone which she found by trailing George for three days, Susan, against his warnings, climbs a tall ladder next to the dinosaur to be closer to him. She tells David that her aunt has given her the million dollars, and she wants to donate it to the museum, but David is more interested in telling her that the day spent with her was the best day of his life. They declare their love for each other, and Susan, distracted by the moment, unconsciously swings the ladder from side to side. As they talk, and the ladder sways more and more with each swing, Susan and David finally notice that Susan is in danger. Frightened, she climbs onto the skeleton, eventually causing it to collapse. David grabs her hand before she falls, lifts her onto the platform, and halfheartedly complains about the loss of his years of work on his Brontosaurus as she talks him into forgiving her. Resigning himself to a future of chaos, David embraces and kisses Susan.
