Four years later, a stranger to this site stumbles upon your post, led by a search for "Rat-a-Tat-Tat the Dancing Cat," or maybe "Rap-a-Tap-Tap the Dancing Cat." Boomerang, you have not lost your mind. It was on "Captain Kangaroo." It was very delicate, and I can still hear the song. It was some type of animation, with cut-outs, I think.