Just don't screw with the Muppet Mafia!
Several years back, I did a show in NYC where I built and performed a dog puppet I built that served as the MC for an out door brass concert, sponsored by PetCo. I built the puppet and wrote the script with the band leader who is my good friend and he really wanted me to voice the puppet like Kermit. The theme of the concert was animals, the band played songs and themes from 101 Dalmations, Jurassic Park, Babe, etc.; and he thought if I talked like Kernit, a gag in part of the show would reference that the puppet's voice "sounded familiar." My character then joked that he had a "famous green cousin" and that was all.
Just to make sure that was okay, I called Henson and asked and they asked if it was being televised. I said no, and offered to send a picture of the puppet I built to show them that it wasn't even a rip off of any dog Muppets, I even asked if they wanted me to do my Kemit impression, but they said it was okay, so long as the concert was free (which it was), it wasn't televised (which it wasn't), and I didn't use the Muppet name, logo or characters (which I didn't). So there's definately a strict protocol on even simple things, but because everything was so simple, and barely referenced, it was okay.