(Michael Buckner/Getty Images for Sundance Institute Los Angeles)

But in the new indie film “Safety Not Guaranteed,” out today in select cities, Plaza branches out to play Darius, an intern at a Seattle magazine who bonds with a story subject, played by Mark Duplass, who’s determined to travel back in time.

The 27-year-old Wilmington, Del., native recently chatted by phone about her work in “Safety Not Guaranteed,” which marks her first starring role. She also touched on several other subjects, including her summer days at the Delmarva beaches; her obsession with Judy Garland; her fervent desire for April Ludgate to get pregnant; and her “unspoken connection” with Bill Murray.

I understand the part of Darius was written for you, but you didn’t know the writers or filmmakers before you worked on this project. Can you explain how that happened?

Plaza: After [screenwriter] Derek Connolly saw “Funny People,” he was inspired by that performance and kind of used it as a jumping-off point for writing Darius. I did know that when I read it. I was very flattered, and then I actually loved the script and the story and all the other characters. I thought it was really well done and funny and that I could kind of do something different with her, but in a really organic way.

At the time, I was looking for something different but something that could show people I can do something more than just roll my eyes, and I thought it was just kind of perfect for that reason. That’s when I get involved and said I immediately wanted to do it. At that time, we tried to get it together but we couldn’t get the money and we couldn’t get the people we wanted. It was only a year or two later that the Duplass brothers got involved and they kickstarted the whole process.

Plaza and Duplass in "Safety Not Guaranteed." (Film District/AP)

This is certainly a more dramatic role than your previous ones. Did you do anything differently to prepare for that?

Plaza: I approach every part the same no matter how small it is or whatever it is. I do a lot of work. I love acting. I’ve loved it since I was a kid. I have an acting coach that I use always. But for this movie, it’s the first movie that I’ve ever been the lead in, where my character has this whole transformation in the film and that has to happen or I don’t think the film will work, if you don’t see her change in the end. So it was a big challenge for me. I prepared a lot. I worked on it for a month. I worked on shooting out of order, being aware of every emotional moment and how that would track scene to scene. It was a big challenge for me, but it’s one that I’ve been dreaming of since I was a kid, so it was really a dream come true, to be able to do that and to really just get in there and make all those moments come to life.

Did you always know that you wanted to be an actor?

Plaza: Oh yeah. For as long as I can remember, that’s what I always wanted to do. I was always doing theater and anything I could get my parents to let me do.

Was there a certain event that sparked your interest in it?

Plaza: I can’t remember. I mean, I know that — I’m sure my parents influenced me. My mom loved movies so much. I’m sure that had something to do with it. I was always watching movies. I would watch them over and over again. I’d watch, like, two movies a day. There were always movies on and we were always going to movies and I think that probably had a lot to do with it.

You grew up in Wilmington, Del. Out of curiosity, did you ever go to the Delaware beaches when you were a kid?

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

I spent my summers at Bethany Beach as well, so I’m wondering if we were there at the same time.

Plaza: Niiice. Yeah, I learned a lot of things on the boardwalks of the Delaware shore — well, the Jersey shore, Delaware beach.

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.

Exactly. So, there’s a moment in “Safety Not Guaranteed” where your character asks another character if he could go back in time, what era he would want to visit. What’s your answer to that? And also, what decade would you absolutely not want to visit?

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.

What era would I not want to go back to? Hmmm. I don’t know. I’m not really that interested in the ’50s. I feel like that would not be fun for a woman to go back to. Or you know, turn of the century, would not be cool ... I think time travel is a pretty cool idea, but when you really think about it, there’s a lot of reasons why you wouldn’t want to go back. Especially as a woman.

The Judy Garland thing — did that 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 — it was like a decade project and 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.

Homework is worthwhile. Really, it is.

Plaza: Yes, it is.

Plaza, Karan Soni and Jake Johnson in"Safety Not Guaranteed." (FilmDistrict/AP)

One of the things I found interesting about this film is that it’s about people wanting to go back in time, not only literally with the time machine, but figuratively as well. Do you consider yourself a more nostalgic person or are you someone who tends to look forward more?

Plaza: I’m pretty nostalgic, I think. I’m pretty ... yeah, I don’t know. I think about the past a lot and a lot of things that have — I’m a worrier, too. I’m always trying to tell myself, ‘You must have no regrets!’ I’m always thinking, if I would have done this, or I would have said this, or if I did this. But ultimately, I’m really happy with where I am. I don’t want to change anything. And I’m always looking to the future. But I try to be a pretty present person and make the best of what is happening now. It’s really hard to do that. But I try.

I understand. So let’s briefly talk about “Parks and Rec” — do you know at this point what might be happening with April next season? Do you have an inkling of what her story arc might be?

Plaza: I don’t know, actually. I don’t even think the writers have all been completely hired yet or brought back yet. So I know that they really haven’t begun that process. I have some ideas that I’m probably not far off [about].

[Note: spoilers ahead] Leslie won the election and that’s going to leave a gap in the parks department, and I have a feeling that April Ludgate is going to have some big responsibilities in the next season, whether it’s taking over Leslie Knope’s position or filling in for her, I don’t know. I think she has kind of grown up on the show and I think that’s only going to keep going as she has to swallow her hatred for everyone and start to command things. I hope.

Plaza with her “Parks and Rec” co-star Amy Poehler. (Fred Prouser/Reuters)

Is there any chance she and Andy might have a family at some point?

Plaza: I don’t know. I want to so bad. I’m always pushing for that. I think it would be so funny if she got pregnant. How funny would that be?

I’d be frightened for the kid. But it would be very funny.

Plaza: I know. I really hope so. I’m pulling for that. I always pull for that. Even in the last season, anytime I would do a talking head, which is where I’m just talking straight to the camera. I would always do my lines and then I would add one thing. I’d be like, “And also, I’m pregnant.” And they’d be like, “Cut! You’re not pregnant. No one wrote that yet.” And I’m like, “Please, please, please.” Yeah, I want that. But we’ll see.

I read a piece about you in New York Magazine in which you talked about a film you just shot with Bill Murray, and how you developed a friendship on-set. I found that interesting because he seems like someone who would be intimidating. I was wondering how you broke through that, or if you found that at all.

Plaza: He’s so intimidating .He’s the most intimidating person to be around because he’s the funniest person in the world and he’s just so interesting and charming. 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 as him, 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 and I was just doing stuff. He walked in to get something in the makeup trailer. 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.

But, no. He’s one of my heroes. Just being around him for even a minute was really special to me.

It’s the eye rolling. That’s why people are intimidated by you. But this movie will change all of that.

Plaza: That’s right.