The ending in the book is a little less happy than in the finished film.
The book ends with Nadya arresting Kermit not just for breaking out of the gulag, but also for stealing her heart, and the Muppets get their prison sentence shortened from several years to just six months in exchange for Nadya having a solo in the finale, and Kermit is happy that it at least gives them time to rehearse and get better. While in the movie, she has Kermit arrested for running out on the revue, the Muppets all ask her to arrest them as well, and she's so moved by them being willing to go to jail with Kermit, making her believe they are family after all, that she lets him free, and they simply go back to jail just as part of their world tour.