There are two sources:
A: we just look for comments on part 8 of "The Great Muppet Caper" on YouTube;
B: Looking on the Soundtrack section of that film article on the IMDB (Internet Movie DataBase).
Actually, YouTube comments and IMDb aren't considered good sources here. Please read Muppet Wiki:Name That Voice (although the page technically applies for Muppet voices).
Just wanted to chime in here. In the recent podcast interview with Charles Grodin, Grodin says that he *thinks* he did the singing, but couldn't actually remember. It certainly does sound like him, but I don't personally think that's enough to say that it definitely is.