Aubrey Plaza has become Hollywood’s poster girl for sarcasm. Many of her roles — as Seth Rogen’s quirky girlfriend in “Funny People,” the obscenity-spewing Julie Powers in “Scott Pilgrim vs. the World” and, most notably, the consistently dour April Ludgate on NBC’s “Parks and Recreation” — have cemented her image as the 20-something woman most likely to say, “Whatever.”

But in the new indie film “Safety Not Guaranteed,” currently in theaters, Plaza branches out to play Darius, an intern at a Seattle magazine who bonds with a man (Mark Duplass) determined to travel back in time.

The 27-year-old Wilmington, Del., native recently did a bit of time-traveling with us during a telephone conversation in which she reminisced about summers at the Delmarva beaches, her obsession with Judy Garland and her recently established “unspoken connection” with Bill Murray.

QAs someone who grew up in Delaware , did you ever go to the Delaware beaches when you were a kid?

Aubrey Plaza as April Ludgatein ‘Parks and Recreation.’ (Justin Lubin/JUSTIN LUBIN/NBC)

Plaza: Oh, yeah — I spent my summers there. I spent my summers at Rehoboth or Bethany Beach or Ocean City.

Did you rent a house when you would go?

Plaza: My parents would always rent a house. They would either rent a house a block from the beach or they would go on the bay side. Some years, we would stay on the bay side and go crabbing and do all that kind of stuff. And then as I got older, senior week started happening. And then you’d go to Dewey Beach and rent a house with your friends and try not to get arrested.

There’s a moment in “Safety Not Guaranteed” where your character asks another character what era he would visit if he could go back in time. What’s your answer to that?

Plaza: I, for the longest time, have been a crazy Judy Garland fan. I mean, I was obsessed with her growing up. It was unhealthy. The first thing I think about is going back in time to see her live or hang out with her or, I don’t know.

I would totally go back to the ’60s and see some of her crazy concerts at the Palladium or something, you know? I’m fascinated by that.

Did the Judy Garland thing start because you saw “The Wizard of Oz”?

Plaza: No, although I do love “The Wizard of Oz.” To be honest, I did this project in seventh grade, I think, where I had to . . . do a report on the ’60s, and I had to profile people that were alive or died during that decade. And I randomly chose Judy Garland because she died in 1969, so I did a whole thing on her. Then I started reading all of these different articles about her and doing all this Internet research about her. And I kept coming up with different explanations of her death, and it just really — I turned into Nancy Drew or something. I was like, “Some people say that she committed suicide. Some people say it was an accidental overdose. What was it? How did she die?”

I don’t know why, but I took that project on myself because I was so fascinated by her, and then I started listening to her music because of that, and then I started watching her movies. I remember seeing “Meet Me in St. Louis” and “A Star is Born” and just feeling completely in love with her and feeling like she was just the most amazing performer that’s ever existed. It all spun from a homework project. So something valuable came out of homework.

I read a piece about you in New York Magazine in which you talked about a film [A Glimpse Inside the Mind of Charles Swann III] you just shot with Bill Murray. You said you developed a friendship on-set. I found that interesting because he seems like he would be intimidating.

Plaza: Yeah, he’s one of the most intimidating people I’ve ever met. I suspect that maybe — I’m not on that level of intimidating . . . but some people, I feel, are afraid of me sometimes. I connected with him in that way a little bit.

We had an unspoken kind of connection, I feel. If I can speak for him. Which I can’t.

You just did.

Plaza: Yeah. I don’t know. The first time I saw him, I was in the trailer, and I was just looking in the mirror. . . .

He walked in and looked at me in the mirror, and I looked at him in the mirror, and we just kind of had a stare-off. We didn’t say anything to each other.

He kind of looked me up and down, and I looked him up and down. He kind of nodded and then walked away. And I was like, well, that’s it. We’re best friends now.

He’s one of my heroes. Just being around him for even a minute was really special to me.