That is definitely from "Auntie Mame" (1958), with Rosalind Russell. In the film, Peggy Cass plays Russell's mousy secretary who writes down everything. I remember that scene exactly as you described it, except she is following Russell, not a man. There is a rich, handsome man involved, and he ends up getting the secretary pregnant (pretty racy for the time!), and the film is indeed a comedy. The film is available on DVD and should not be hard to find.