It was exhilarating to be on ‘SNL,’ but sketches can be very transient,” Amy Poehler says. “The show was an amazingly exciting machine that you jump on and ride. It’s fun to work another muscle and do a lot with a character.”

That’s how Poehler explains why she’s happy to be playing Leslie Knope, the goodhearted, ambitious but ineffectual small-town political operative at the center of NBC’s “Parks and Recreation,” the new mockumentary series from “The Office” vets Greg Daniels and Michael Schur. Poehler manages to make Leslie endearing with a performance deftly ranging from zany to vulnerable in each episode.

“Having three dimensions is kind of important,” Poehler says. “Leslie has a lot of different dimensions. It’s fun to sit down and think about how she’d react to situations, what she’d do and not do.”

After eight years as a versatile performer on “SNL,” impersonating everyone from Hillary Clinton to Dakota Fanning as well as creating her own characters and co-anchoring the venerable “Weekend Update,” Poehler left the show in grand style, performing a witheringly hilarious rap song about vice presidential candidate Sarah Palin. A week later, Poehler gave birth to her first child, Archie. Mere weeks later, she was at work on the set of “Parks and Recreation.”

Poehler, a former member of improv troupe the Upright Citizens Brigade, is able to apply her improvisational skills to Leslie’s assorted quandaries in “Parks and Recreation.”

“I love the way we shoot,” she enthuses. “We do seven, eight pages a day. There are a lot of quick setups. We do a lot of takes and get to improvise a lot. Her situations suggest things that we can try on the fly. Certainly, the form lends itself to that.”

What do you like most about your character?

“There’s nothing cool about her. It’s fun to play someone who’s well-intentioned but doesn’t know the game. I enjoy competent but misguided characters. She’s an open-faced sandwich, and because of that, she doesn’t have anything savvy about her.”