Klein is Cloudy. Or rather, Federal Agent Klein—the upright, dutiful gent to brassy, snarling Mulderig—is played by Buddy Grosso, the real-life Cloudy.
And, notably, the two roles are similar. If Mulderig and Popeye are the impolite fighters, Cloudy and Klein are the ones always looking for a little reason and balance in their partners' chaotic style.
As with the other minor characters, Klein works mostly as a plot device, like when he's tailing Charnier and Sal to DC to keep the boys back in the Big Apple abreast of the situation. He shows up when it's convenient and fades into the background when it's not.