If anyone can be counted on to be unimpressed by the hype at South By Southwest, it’s Aubrey Plaza.

“The interactive thing, what is it?” asks Plaza, contemplating the dominant third of SXSW’s overlapping film, music and interactive conferences. “Do you like go and interact with a robot or something?”

That might sound like the droll sarcasm that has often defined Plaza’s deadpan performances in the NBC comedy “Parks and Recreation” and Judd Apatow’s “Funny People.” And that’s undoubtedly a characteristic of Plaza, but the persona has been so convincing that many presume Plaza is no different from those roles.

In the film that has brought Plaza to SXSW, the earnest comedy “Safety Not Guaranteed,” Plaza’s character undergoes a shift. She plays a Seattle magazine intern who becomes enmeshed with a story subject, an oddball named Kenneth who believes he can time travel (Mark Duplass). Her disaffection slowly breaks down, won over by Kenneth’s idiosyncratic warmth.

“When I read the movie and saw the transformation that she goes through, I was like, `Yes, that’s exactly what I want to do,’” says Plaza. “The movie’s kind of a weird metaphor for me as an actor, because at that point, I was definitely looking for something to show people that I have range and can do other things.

“It’s like I kind of slowly rip the Band-Aid off during the movie.”

Plaza, a 27-year-old Delaware native, was a comedy nerd at an early age. She found her way to an internship at “Saturday Night Live” (she later auditioned but pulled out for other opportunities) and became a fixture at New York’s improv bastion, the UCB Theatre.

The first time Plaza was seen as the eye-rolling sort, similar to MTV’s “Daria,” was the Web series “The Jeannie Tate Show” by Maggie Carey, wife of “SNL” cast member Bill Hader. She played the teenage daughter of a soccer mom hosting a show from her minivan.

“Before that, it wasn’t a thing that I did, really. It wasn’t like I was known for being `sarcastic person.’ I was doing a ton of characters at UCB. It was just something I did in that Web series, and then off of that, I got a couple things in a row,” says Plaza. “It’s part of me, also. But it just one part.”

Those other opportunities came in a bizarrely condense window. In the same week, she landed her character, April Ludgate, on “Parks,” the part in “Funny People” based on a young Janeane Garofalo, and a co-starring role in Edgar Wright’s “Scott Pilgrim vs. the World.”

At first, her character on “Parks” was almost entirely limited to eye-rolling and vacant stares. But as the show has gone on (it recently wrapped shooting of the fourth season), April has increasingly broken her hard front, often in hidden smiles to the camera. The subtle flashes of April’s interior are all the more impactful because they’re so rarely parsed out.

“If that’s all it was – just deadpan, sarcastic, depressed with nothing going on underneath of it – that might get old really fast,” says Plaza. “But it’s fun to kind of play that and have a lot of stuff brewing underneath and show it sometimes. But it’s very withholding. I’m very withholding, and it’s working, I guess.”

She laughs and adds she has nothing against pure deadpan, either: “It’s fun to pretend like you hate everyone and you don’t care about anything.”

“Safety Not Guaranteed,” which opens June 3, received a rapturous response Saturday night at SXSW. Though it’s a laugh-filled comedy, it stretches Plaza dramatically. It’s very possibly her most open performance.

“I feel like you really see Aubrey growing up in this movie,” says Duplass, who’s also a producer. At the premiere, Duplass said it’s not until their characters meet – and Plaza improvises an awkward response – that the movie clicks.

Whereas Plaza’s characters seem far too cool to ever experience anything like nervousness, the actress has spoken about her battles with anxiety. She suffered a stroke while in college at New York University. She says she’s gotten better about handling it.

“I’m totally different than I was a couple years ago,” she says. “I’m able to recognize when I’m having a panic attack and talk myself out of it. I’m pretty OK right now. No medication necessary. Living in L.A. is kind of good. I’m just healthier. As I got older I realize the value of exercise and all that boring s—.”

“Safety Not Guaranteed” – which Derek Connolly, a friend from NYU, wrote with Plaza in mind – was made while “Parks” was on break last year. Of the other films she made at the same time, perhaps most intriguing is “The Hand Job,” written and directed by Carey and co-starring Hader. Plaza calls her character, a type-A Valedictorian – a “total 360″ for her.

On this break from “Parks,” she hopes to shoot two movies and focus more on writing. She’s writing a young adult novel for Penguin’s Razorbill based on her high school experience.

Asked if audiences have yet seen a character particularly similar to her off-screen self, Plaza replies: “Not really. Not yet.”

Then she adds with a smile, “But I also don’t know who I am.”

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