Dr. Robert McDonald moves the beautiful robot Rhoda Miller into his apartment and begins the task of training her how to function in the human world, while keeping her secret from being discovered, a situation complicated by his interfering sister and his lovesick neighbor Peter.
When Space Agency psychiatrist Bob McDonald finds a top secret prototype female robot, her creator Dr. Miller asks Bob to take over her care and training when he is reassigned to Pakistan.
Reading Lewis Carroll's "Alice in Wonderland" has had a peculiar effect on poor Rhoda. She's afflicted with spells of vertigo, as well as difficulty distinguishing fantasy from reality. The situation is complicated by an unexpected visit from Bob's boss.
It would take a computer to find the right girl for Peter, and Bob has just the tool, Rhoda. He furnishes Rhoda with information on 250 girls working at the space lab, trying to find a match for Peter.
Bob's friend Herbert would rather be a comic than a pharmacist, but he's not a very good comedian, so Bob has been asked to persuade the young man to stick to filling prescriptions.
Peter owes a small fortune to a pool shark, but he very cleverly signed Bob's name to the IOU. They send in Rhoda to play the pool shark and with her abilities beat the shark and repays the debt.
Bob gets off to an inauspicious start as chairman of a road-safety committee by crashing into his neighbor's car, then Rhoda testifies in court about the entire incident.