Check this out; This is where they keep Photos, scripts, posters, tapes and other stuff from the 'Live' Muppet productions:
http://www.cah.utexas.edu/findingaids/vee.html
Then right here at MC there is an interview with Jim Henson by Judy Harris where she asks him about where they keep the Muppets. The following is an excerpt from the last page pf the interview (
http://www.muppetcentral.com/articles/interviews/jim4.shtml):
In 1978 there were over 500 Muppets, so there must easily be many more by now. Do you have any idea how many Muppets there are?
HENSON: You know, I don't really know. I couldn't begin to guess actually.
When they're not being used, are they all in your various buildings on 69th Street - is that where they're housed?
HENSON: No, we have a lot of storage - we have theatrical storage in New York because we built up - they're quite bulky, you know, particularly the large characters, and so we couldn't begin to store all the stuff in our place.
So how do you keep track of them? Is there some one place where they're all inventoried?
HENSON: Yeah, yeah, we have boxes and they're all carefully labeled and that sort of thing, and we do go back and pull them out for other shows.