The Nasty Rabbit (1964)

Soviet agent Mischa Lowzoff arrives in America with a rabbit bearing a vial of dangerous bacteria. His orders are to free the rabbit on the Continental Divide, from which the germs will spread, killing millions of Americans. Disguised as a cowboy, Lowzoff arrives and boards at a dude ranch, where his movements are observed by similarly disguised agents from England, Germany, Mexico, Japan, and Israel, and by the ranch's owner, an undercover agent for the FBI. The landlord joins forces with singer Britt Hunter, a Pentagon employee, to deactivate the deadly capsule.