Here's the late great Ralph Bellamy talking about the making of The Awful Truth. About two or three minutes into the clip, he describes Leo McCarey's method of working: he had no script, the actors didn't really know what the story was from moment to moment, and he threw the actors into scenes without any preparation. The first scene Bellamy shot was singing "Home On the Range" with Irene Dunne at the piano: Bellamy couldn't sing, Dunne couldn't play the piano very well, and that's exactly what McCarey wanted.
Even today, when improvised comedy is more legitimate and respected than it was in 1937, can you imagine anyone making a film like this? Even an independent film? In his prime, McCarey was so well-respected by the studio bosses that they would let him make a film without a real script; according to Bellamy, Harry Cohn left McCarey alone and trusted him to make things turn out right, even when the actors all complained about him.
And here's the "Home On the Range" scene.