Fosse was co-choreographer on Bells Are Ringing. According to more than one of the Robbins and Fosse books, Robbins was unhappy with Fosse's work on Bells Are Ringing, feeling that Fosse seemed to be trying to imitate Robbins, and he wanted a first-rate Fosse rather than a second-rate Robbins. "Mu-Cha-Cha" was largely or completely the work of neither. Robbins allowed Peter Gennaro to choreograph it, and that led to Gennaro being hired for West Side Story.
EDIT: Yes, it is a good example of that kind of number, put in with Robbins's approval even though he didn't stage it.
