Actress Amy Brenneman

Amy Brenneman stars in HBO Warner Brothers new series "The Leftovers," premieres June 29. (Paul Schiraldi, HBO / July 10, 2013)

It's good to hear Amy Brenneman's voice on the phone.

That's because in her surprising new role on HBO's dramatic series "The Leftovers, " her voice isn't heard at all, anytime soon.

In it, the Glastonbury native, whose work has included "NYPD Blue," "Judging Amy" and "Private Practice," plays a member of a sect that takes a vow of silence, wears white, lives communally, chain smokes cigarettes and provides a haunting and controversial presence for residents of a small town.

The sect — the Guilty Remnant — is created in response to the story's central calamity: The day, suddenly, three years back, when 2 percent of the world's population disappeared. Whether it's due to a Rapture-type event or something else, nobody seems to know.

The source material for "The Leftovers" is the novel of the same name by Tom Perrotta ("Election," "Little Children") that is being adapted by writer/producer Damon Lindelof, in his first big project since TV's "Lost."

Brenneman says Lindelof is the main reason she signed onto the series, which begins June 29 on HBO.

"I just was utterly captivated by him," she says during a recent interview from New York. "I'd watched 'Lost.' Although I wasn't a diehard fan, though I certainly knew his capabilities. It's like he had me at hello, because he said, 'Here are the reasons you shouldn't play this role.'

Among them: "You don't speak, you don't wear makeup, and it shoots in New York.' And I was like: Yeah, I'm in."

It was a matter of facing challenges when they come along, says Brenneman, 49, who is raising two children with her husband of 19 years, director Brad Silberling. "It's so thrilling to do something you've never done before and have never seen anybody else do before."

It is odd in some ways not to talk in a role, she says. But, she adds, "I enjoy being silent on film. I love listening to people on film. It's one of my favorite things to do. So I thought: that's not going to be a problem. And I certainly trust my face to communicate whatever it needs to communicate.

"It also crossed my mind a number of times that it's probably good that I don't do Botox because I literally could not express anything," she adds. "So my face is very mobile, and it needs to be, because it needs to reflect every nuance and idea."

Because she can only communicate with others by writing notes, Brenneman finds herself in a role in which she has to pay more attention to penmanship than articulation.

"I think what got more difficult was: I play a pretty complex woman," she says. "I take actions that are very complicated, that are kind of controversial. I have to understand why I'm doing it. A lot of what I do is really not liked by other people."

That in itself is unusual for her, she says.

"Usually I want the audience to understand me and to like me and sympathize with why I'm doing this," she says. "Obviously, I had to let go of this pathological need to be liked, number one. And then I just had to figure out a different way to communicate all of those things."

And what is her take on this character, Laurie, that she plays?

"I definitely have a sense of why she made the choice to join this group," she says.

And because the story picks up three years after the mass disappearance, there are likely to be flashbacks to show the reason for her joining.

But for now she says, "I think that in a world that where you're in a completely unprecedented situation in human history, all decisions are valid in a way because nobody can tell you what the right way to go is.

"But there's lot of chatter and insanity and violence that happens in the wake of this. And I think at a certain point, Laurie just says no. I'm going to live like a monk. I'm not going to participate in this or engender more of this. So I drop out."