Written by Samy Burch from a story by Burch and Alex Mechanik, both making their feature debut, “May December” from director Todd Haynes of “The Velvet Underground,” “Carol” and “Far From Heaven” fame is an odd bird. But then again Haynes has made a career out of odd birds. Haynes once made a short film about Karen Carpenter, using Barbie and Ken dolls as his “actors.” It worked remarkably well.

This new film tells the story of a fictional actor named Elizabeth Berry (Natalie Portman), who visits Savannah to study a married couple for a film she is about to shoot. The film is about the couple, who made news over two decades years earlier when they had an affair when the woman was in her 30s, married with children, and the man was 13. She went to jail. When she got out they got married and had children of their own. Elizabeth arrives on the eve of the high school graduation of two of the children. The film is loosely based on the story of Mary Kay Letourneau.

The household is in a tizzy. Young patriarch Joe (a handsome Charles Melton) is cooking a barbecue for the family and friends. Elizabeth arrives carrying a box from the mail that Gracie Atherton-Yoo (Academy Award winner and frequent Haynes’ collaborator Julianne Moore) and Joe immediately recognize as containing something repugnant. They used to get many more of them, Gracie shares.

How does an actor become someone else for the camera? “May December” asks, especially if the character is a real, living human being. Is there some magical transference that occurs. Or is the process more like a research paper? Haynes once had Cate Blanchett pretend to be Bob Dylan in his 2007 effort “I’m Not There.” “May December” will also remind film buffs of Ingmar Bergman’s “Persona,” the iconic 1966 personality-switching classic featuring Bibi Andersson and Liv Ullmann as two women whose personae begin to meld.

In “May December,” the melding is not nearly as dramatic. Elizabeth, who is meticulously polite, watches Gracie and Joe and asks questions. Joe and Gracie were caught in the act in the stockroom of a pet shop where they worked. Elizabeth goes there and questions the nervous, long-time owner. She asks to see the stockroom, where, alone, she plays at recreating Gracie’s and Joe’s love scene. She has read the old scandal sheets. She visits the high school that Gracie and Joe’s daughter Mary (Elizabeth Yu) and their son Charlie (Gabriel Chung) attend. The star of a popular TV series, Elizabeth is recognized by some of the students.

For Gracie, who seems about to have a nervous breakdown, the past hardly exists, or so she claims, even though she has an ex-husband and their children living nearby. Elizabeth allows that the past weighs on her. Joe, who rather too symbolically raises monarch butterflies, all is good with him if his wife and children are happy. The rather disturbing piano you hear in the background is a Michel Legrand score for the 1971 Joseph Losey film “The Go-Between” rearranged by Marcelo Zarvos.

It adds seriously to the film’s jumpiness. Gracie and Elizabeth encounter one of Gracie’s “other” children at a local luncheon spot, where he fronts a cover band. Joe’s aging father fills an ashtray with burnt butts. At a class at the high school, a nasty boy asks Elizabeth about “sex scenes,” something I found terribly unlikely. She observes that playing bad people is always more fun. Gracie, who works from home as an artisanal baker, keeps telling Joe to move his “bugs.” Elizabeth tries her Gracie impersonation in front of a mirror, and it is very good. Gracie and Joe’s oldest child Honor (Piper Curda), expressing a sentiment viewers are bound to wonder about, wishes the movie was not happening at all. I mean, right? “May December” ‘s dirty laundry is hard to clean.

(“May December” contains nudity, drug use and profanity)

“May December”

Rated R. At the Landmark Kendall Square. Grade: B