I could not find any stooge connections except Abbott and Costello.
It's a distant Stooges connection, but in her 1941 movie "Andy Hardy's Private Secretary" Kathryn Grayson sings the Johann Strauss waltz "The Voices of Spring", which is of course very much identified with The Three Stooges due to Christine McIntyre's memorable performance of the song in the Stooges short "Micro-Phonies".