"I am the daughter who dies," said Michele Greene.

Because she is, she'll turn up in only the first half of NBC's "To My Daughter" airing Monday at 9 on NBC.

That leaves the movie to the survivors, mainly Rue McClanahan in a dramatic role far different from that of Blanche in "The Golden Girls."

It's a story about relationships among a single mother and her three children. The strongest bond is between Laura Carlston and her eldest child, Julie, 28, a television screenplay writer who is working on a book. Considerably weaker are the ties between Laura and Bobby (Ty Miller), 21, and 18-year-old Anne (Samantha Mathis).

The script is based on real events.

"It's about a family who is traumatized by the death," said Greene. "You know how television, especially, portrays families -- as sort of idyllic: The parents have heart-felt conversations with their children, the way people in real life don't really do with their children.

"This movie is uncompromising because it shows the way parents favor one child. There's one they give more of their emotional life to -- they'll never admit that. My character and Rue McClanahan have this incredibly tight relationship and she's sort of left to repair the damage. It's a painful movie in many ways."

When Julie dies, Laura, a high school English teacher, suffers emotionally, but decides to complete her daughter's book. As they have been all their lives, the younger son and daughter continue to be ignored, living in the shadow of their sister's death as they did while she lived.

Greene said that this role and one in USA Network's recent "Nightmare on the 13th Floor" are part of her effort to avoid being stereotyped as single-mother lawyer Abigail Perkins on NBC's "L.A. Law."

"When you're on a series, you want to make sure you do stuff so you don't get locked into a stereotype," Greene said. "But still, there is a real desire to do other things. Cable is strange. I like cable. It's sort of an exciting netherworld."

In "Nightmare," which aired on Halloween, Greene played a travel writer who witnessed a man being hacked to death with an axe on the building's 13th floor, which had been sealed off after a mass murder by a Satanist in 1900. Then she became a target of the killer.

"I kind of liked it, because I've never done one of those horror stories. I've always wanted to do one. I've always wanted to do a western, too. The thing I liked about the script was I have this fascination with hotels. They're weird. That one took place at the Ambassador Hotel, which is an incredibly creepy hotel. There's something sort of depressing about it. The hotel is really big. There were three other film companies {working there} and we never saw them at all."

Still, almost since she was graduated from the University of Southern California, "L.A. Law's" Abby Perkins has been Greene's ticket to success. For the 1988-89 season, she won an Emmy nomination for the role, along with Susan Ruttan, who plays Roxanne Melman on the series. Playing Abby Perkins has also enabled Greene, who is 28 and single, to own a home in Hollywood Hills.

Before "L.A. Law," Greene turned up in a CBS summer comedy series called "Dorothy" that had four outings in 1979 and in NBC's "Bay City Blues," which aired three times in 1983. She also appeared in a daytime special, "Andrea's Story: A Hitchhiking Tragedy"; in several TV movies, "Matlock" and "Perry Mason: The Case of the Notorious Nun."

On "L.A. Law," Abby Perkins seems especially vulnerable, in contrast to other women lawyers at McKenzie, Brackman.

"Actually I like Abby Perkins," Greene said. "There's a lot of things about her life that are sort of unexplored."

One of them, said executive producer David E. Kelley, will be her life as a parent. This season's opener included a scene in which Perkins took her 9-year-old son to a baseball game.

A couple of seasons back, when Abby Perkins took a case involving a battered wife, viewers learned that Perkins too had been a victim of spouse abuse. Another case, when she was briefly in private practice, ended with her client crashing through her office door to attack her. She grabbed a gun from her desk and shot him.

The vulnerable Perkins' opposite number last season was hard-driving attorney Rosalind Shays (Diana Muldaur).

"What a kick!" said Greene. "I loved her. We hit it off right away. Diana Muldaur is so nice and so fun, a great sense of humor. It was great having her around all year."

She said she's also fond of "L.A. Law's" Jimmy Smits, who plays Victor Sifuentes and who, like her, comes from a Latino background. She said she'd like more scenes with him, but said they are rarely paired partly because Smits is about a foot taller and twice her weight.

ABC had said the two were scheduled to appear on an installment of "Cop Rock" last week, before that network announced it was canceling the series.

Born in Las Vegas (her father died when she was an infant), Greene and her brother grew up in Southern California where her mother works as a real estate agent. From her mother, whose relatives live in Mexico, Greene speaks fluent Spanish. She has done volunteer work in Mexico with a public-health project, helping to construct toilet facilities, and works with a group arranging medical aid for Salvadoran children.