Mr. Peabody and the Mermaid (1948)

As told to a psychiatrist: Mr. Peabody, a middle-aged Bostonian on vacation with his wife in the Caribbean, hears mysterious, wordless singing on an uninhabited rock in the bay. Fishing in the vicinity, he catches...a mermaid. He takes her home and, though she has no spoken language, falls in love with her. Of course, his wife won't believe that the thing in the bathtub is anything but a large fish.