A Double Life (1947)
This is a remake of the film.
Coleman exclaims "Oh, the tricks your mind can play," a lyric from the song "Where or When" written for the musical play on which this movie is based.
Mentioned by Osborne in Dinah Shore clip with Shelley Winters.
Movie reviewed in this episode.
Comic variation where a white actor portrays a black character and the actor gets lost in the role he's playing