A paleontologist is kept from his wedding by an odd-ball woman with a pet leopard.
Paleontologist David Huxley (Cary Grant) learns they found a rare dinosaur bone and kisses his fiancé Alice Swallow (Virginia Walker), who lectures him that only his work is important. While playing golf, David asks Alexander Peabody (George Irving) for a million dollars; but Peabody is only Elizabeth Random's lawyer. Susan Vance (Katharine Hepburn) hits David's ball and drives his car into a car and a tree. Susan drops an olive, and David slips on it. Psychiatrist Fritz Lehman (Fritz Feld) tells Susan that David is following her because of a fixation. Susan gives David a lady's purse and tears his coat. He stands on her skirt, ripping off its back. Susan sews his coat and drives him to Peabody's house. Susan hits Peabody with a pebble.
David's bone arrives, and Susan calls that she got a leopard named Baby and asks for his help. David rushes over and leaves, but Baby and Susan follow him. So Susan drives them and hits a poultry truck. David buys meat for Baby, and Susan steals the car with Baby. While David takes a shower, Susan sends out his clothes to be cleaned. David puts on her robe. Elizabeth Random (May Robson) comes in with a barking dog named George, who takes the bone. Susan realizes she is in love with David. They look for the bone and ask George, who digs up boots. David calls Alice, having missed his wedding. Major Applegate (Charles Ruggles) comes in, and Susan says that David is Mr. Bone, a hunter. The gardener Gogarty (Barry Fitzgerald) drinks and lets Baby out. Major Applegate makes a leopard call. Gogarty sees Baby and panics. David calls the zoo but learns that Baby belongs to Elizabeth. Major Applegate shows Elizabeth the leopard call and sees Baby.
Susan and David search and see Baby playing with George. David and Susan get wet in a stream and dry off by a fire. A circus transports a dangerous leopard in a truck; but Susan lets him out. Major Applegate shoots, and Elizabeth stops him, saying it is tame. Major Applegate and Gogarty run from the dangerous leopard. David tells Susan to go home, and she cries until he says she can stay. They sing to the leopard on the roof. Dr. Lehman assumes she is crazy, and constable Slocum (Walter Catlett) arrests David and Susan. Gogarty is put in jail too. Elizabeth demands her niece, but she and Major Applegate are locked up also. Susan acts like a gangster, offering to talk, and slips out the window. Peabody and Alice find Elizabeth and David in jail. Circus men are followed in by Baby, and Susan drags in the other leopard on a rope. David protects her and gets it into a cell before fainting. At the museum Alice leaves David, and Susan brings in the bone. David tells Susan to go away, but she climbs a ladder and says she has a million for the museum. David says he loves Susan, who causes the brontosaurus skeleton to collapse.
In this bizarre comedy Susan finds peculiar ways of keeping David from attending his wedding while he is irresistibly drawn to her even though she causes him nothing but trouble.