Originally Dave Goelz wasn't comfortable with Zoot. He couldn't quite figure out the voice and personality, so whenever Zoot had lines, Dave would try to hand them off to another character. Well after awhile, Zoot just had a reputation for being the saxaphone player who didn't really talk much at all. People started coming up to Dave saying "I know a saxaphone player who's just like Zoot," so Zoot just sort of stayed relatively silent. However, off the top of my head, I can think of at least two full sentences he has said:
1.) "Oh, he's just upset about missing the Rembrandt exhibit at the National Gallery"- The Great Muppet Caper, talking to Kermit, refering to Animal.
2.) "Hey man, I can't figure out what side we're on. Are we with the pirates, or the frog captain?"- Muppet Treasure Island, talking to Floyd, refering to... um... well, he sort of sums it up himself...