Stewart had been a guest on the WCBS radio show in March of 1957, and now he was back for a second visit with host Bill Leonard. The date was May 30, 1958. Here is the New York Times listing for the program.
Stewart seems to have been wedged in between a sculptor and an author. The show is not available, but since Stewart’s latest film, Vertigo, had its New York premiere on May 28th, it is probably safe to assume that he talked about his new film.