February 01, 1988 12:00 PM

Some actors polish their skills in class, others onstage, but Rebecca Miller’s training ground was the 350-acre Connecticut farm where she grew up. When her father, playwright Arthur (Death of a Salesman) Miller, and her mother, photographer Inge Morath, were busy, their only child would make herself weird headdresses, go into the woods and tell herself stories. Or she would corral friends to put on a Chekhov or a Giraudoux play, with sets and costumes, in the barn. “My father thought I was a bit of an eccentric,” says Miller, 25. “But because I worked very hard, it was fine with him.”

This week she makes her TV acting debut in the NBC miniseries The Murder of Mary Phagan, which tells the true story of Leo Frank, a Jewish factory manager in Atlanta and victim of anti-Semitism who was convicted of murder in 1913. Peter Gallagher, who plays Frank, was instantly charmed by newcomer Miller in the role of Frank’s loyal wife. “She was a little anxious at times,” he says, “but it was always about the substance of the scene, rather than ‘How can I look best?’ ”

Similarly impressed when he met Miller at an audition last fall, director Peter Brook cast her as Anya in his highly touted production of Chekhov’s The Cherry Orchard, now in a three-month run at the Brooklyn Academy of Music. Considering that this was Miller’s first stage role since a high school production of her father’s play The Crucible, she does seem to inspire an unusual amount of confidence. About a year ago top theatrical agent Sam Cohn met Miller at dinner with her parents and persuaded her to try acting. “As a painter, I had been a hermit, and I thought it was time for a different kind of life,” says Miller, who won her TV role at her second audition.

One of Rebecca’s greatest challenges as an actress has been stepping out of her 72-year-old father’s long shadow. Miller was married to Marilyn Monroe before he wed Morath, 64, his third wife, in 1962. Talk of MM leaves Rebecca visibly annoyed. “The subject of Marilyn Monroe does not interest me,” she says. Rebecca continues, “People want to think that my father could pick up the phone and get me a job. He wouldn’t do it if you had him hanging by his toenails.”

Even if Arthur did want to meddle, chances are his daughter wouldn’t allow it. “Someone asked me if I thought she should become an actress,” Rebecca’s father recalls. “And I said, ‘It’s about 20 years too late to answer.’ She’s always been very independent.” In any case, he does approve: “Apparently she has a terrific sense of where the truth lies in a scene. And she looks marvelous. That doesn’t hurt either.”

Rebecca credits her mother for training her to be at ease before a camera. “It was as if her nose were a lens,” Rebecca says. “It felt natural to pose for her.” In fact Rebecca was more comfortable with her parents than with other children. They encouraged her artistic bent.

She studied painting at Yale, graduating in 1984 and later winning a four-month visiting artist fellowship from the Munich Ministry of Culture. She spent the next three years creating odd-shaped oil paintings and altarlike cabinets that house video screens showing rhythmic film clips. “I’m fascinated by dream images,” says Miller, who will open a one-woman show in August at a Connecticut gallery. “Sometimes the images are difficult to decipher, but the texture, color and movement make them compelling.”

In the shabby Manhattan hotel room where she lives, Rebecca looks more like an art student than an actress. She wears paint-spattered duck boots, sweatpants, a baggy mohair sweater and no makeup. Having ended a five-year relationship with a musician last fall, Miller keeps to herself except for occasional visits with other artists or Yale friends. “When I come home from work, I need to have thinking time,” she says, though she doesn’t plan on a lifetime alone. “I want to have a brood, but not right now.”

One of the subjects Miller ponders during her solitary nights is whether or not she will continue with her acting. “I think primarily she wants to be a painter and will stick with it,” says her dad. His daughter concurs. “It’s not as though I’m making a career out of acting,” says Rebecca, who clearly finds self-sufficiency more of a lure than fame. “My parents taught me that success in terms of other people’s opinions of you is a fickle thing. My tiny little successes—I welcome them. But I don’t give them too much weight. Tomorrow they could be gone.”

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