Uniform Stealing Board

Not sure if this scene really qualifies for USB, since (1) it's a replacement instead of a clothes steal and (2) the knockout/replacement is unintentional. It's an old sitcom episode where Joan (played by Joan Davis) accidentally knocks out a female acrobat (while wearing similar clothes) and is mistaken for her onstage.

You see the real acrobat at the beginning of the clip. Knockout about 2 minutes in.

https://www.youtube.com/watch?v=MYU0x1DlJ-M