The skit features SNL castmember Fred Armisen as Paterson during a segment on "Weekend Update."
Like disgraced Illinois Gov. Rod Blagojevich, Paterson must appoint someone to the senate seat being vacated by Sen. Hillary Clinton. Blagojevich was arrested last week for trying to sell the seat left open by President-elect Barack Obama.
Armisen, as Paterson, says he has three criteria: economic experience, upstate influence and someone with a disability who is completely unprepared for the job - just like him.
"I want to choose a senator not from the glitzy coke parties of Manhattan but rather from the shabbier coke circles of upstate new york," he said. "I'm tired of all these fancy, two-eyed smart alecs from the big city running the whole show."
"It's time we get someone from Utica, Syracuse or Schnectady - towns where people have something a little off about him. I mean, they don't have to be blind," he said. "I just need someone with like a gamey arm or maybe the giant gums with the tiny teeth. Let's get one of those in the Senate."
The fake Paterson points out that he only became governor because of former Gov. Eliot Spitzer's prostition scandal.
"Whoever is appointed senator must - like me - be caught totally off guard and be comically unprepared to take office," he said. "Come on, I'm a blind man who loves cocaine who was suddenly appointed governor of New York. My life is an actual plot from a Richard Pryor movie."
Paterson also holds up a chart illustrating job losses in the state - but holds it upside down.
Later, he wanders in from of the camera during SNL cast member Amy Poehler's announcement that she is leaving the show.
"Governor, you're in our shot," she said.
The governor's office is expected to release a statement reacting to the skit later today.