When Elizabeth Strout attended an advance screening of HBO’s miniseries “Olive Kitteridge,” a network staffer handed her a package of tissues.

“I thought, ‘Oh, please, I wrote this, I’m not going to need these,” said Strout, whose Maine-set novel “Olive Kitteridge” won a Pulitzer Prize in 2009. “But I did need them. I was aware I had come up with this, but (the film) is so much its own thing that I’d lose myself. Then I’d say, ‘Oh right, of course that happens.’ ”

The four-part miniseries “Olive Kitteridge” stars Oscar-winner Frances McDormand in the title role and will premiere on the HBO cable network Sunday at 9 p.m. Two one-hour episodes will air Sunday, and two more will air Monday at 9 p.m.

Strout, who grew up in Harpswell, says that having her book made into a miniseries has been “wonderful” mainly because she hasn’t been very involved. And when she has been involved, actors and others involved sought and welcomed her thoughts.

Strout visited the set of the miniseries while it was being filmed on Cape Ann in Massachusetts.

“I spoke to Frances a number of times and we just chatted about who I thought Olive was and who she thought Olive was,” said Strout, 58, who lives much of the year in New York but also has a home in the midcoast. “But Frances played it her own way, she made it her own.”

There were things McDormand did on screen as Olive that Strout said she would never imagine Olive doing. Like when Olive is on her way to her son’s wedding, and she’s seen belching.

“I would never have thought of Olive doing that. So I asked the screenwriter where that came from, and she said, ‘I wrote that thinking of my mother; my mother is an Olive character,'” said Strout.

Strout’s novel is set in the fictional small town of Crosby, Maine, and focuses on a retired school teacher and her husband, Henry. The novel explores the people and character of the small town through linked short stories. The miniseries is divided into four episodes, titled “Pharmacy,” “Incoming Tide,” “A Different Road,” and “Security.”

McDormand is an actress whose roles have ranged widely. She won the best actress Oscar in 1997 for playing a steadfast police officer investigating weird and brutal happenings in “Fargo.” For this miniseries, she is reunited with director Lisa Cholodenko, who also directed McDormand in the 2002 film “Laurel Canyon.” In that film McDormand plays a fiery Los Angeles record producer dealing with her adult son and a turbulent romance.

In “Olive Kitteridge,” Olive’s husband is played by Richard Jenkins, whose resume includes the HBO series “Six Feet Under.” Bill Murray has a supporting role in the film, as Jack Kennison, a widower.

“Richard Jenkins is just amazing,” said Strout. “Seeing the film and how it came out was a huge relief for me. It could have been a disaster.”

Actor Tom Hanks, as well as McDormand, are listed among the film’s four executive producers.

This is not the first time a book by Strout has been the basis of a film. Her 1998 novel “Amy and Isabelle” was made into a TV movie by Oprah Winfrey’s studio, Harpo Films. It starred Elisabeth Shue and aired on ABC.

Strout says there are no plans yet for anyone to film her latest novel, “The Burgess Boys.” The book focuses on two brothers who become lawyers and leave their Maine hometown for New York City, only to be called back when their nephew gets into trouble for throwing a frozen pig’s head through the door of a local mosque.

The story is set in Shirley Falls, a mill town very much like Lewiston. Strout based the pig’s head events in her book on an actual incident that happened in Lewiston in 2006.

Strout thinks “The Burgess Boys” would be an easier book to make into a movie than Olive Kitteridge, but she’s not pushing too hard for that to happen.