Hey, Rookie(1944)

Musical comedy star Jimmy Leighter wants to get away from show biz and his leading lady Winnie Clark, so he joins the Army. There he gets the order to put on a show, Winnie Clark appears in a camp show, hears about his task and offers him his help. He thinks, she does it for her publicity only, so he doesn't want to know anything about this, till he finds out, that she has no such intentions.