"Governor Chris Christie from New Jersey announced the construction of a maple syrup pipeline from Vermont," he joked.
The late-night star then turned his attention to Booker, who has recently drawn attention for conversing with an Oregon stripper over Twitter.
"I know what you are thinking, 'New Jersey strippers aren't good enough?' " Letterman joked.
Letterman tried to tie the joke in with former Rep. Anthony Weiner (D-N.Y.), but he flubbed the line. The host originally said that Weiner's wife apologized for Booker's actions out of habit, a punchline that confused the crowd.
"Wait a minute, let me go back," Letterman said. "What did Mrs. Anthony Weiner do?"
He then leaned in to read the cue card and delivered the correct joke, drawing a roar of laugher from the audience.
"[Out of habit], Mrs. Anthony Weiner forgave Mayor Booker," Letterman said in his mulligan attempt. "Now I get it, sure."