NEW YORK, NOV. 6 -- The neighbors in Greenwich Village say they tried to warn the authorities. The social workers say they found nothing remiss. The police say they visited the apartment but the mother would not press charges. The teachers say they noticed the girl's bruises but were told that the cause was a childhood scuffle.

In the end, the system failed 6-year-old Elizabeth Steinberg. She was declared brain dead Thursday, three days after being hospitalized. Her adoptive father, who police say beat her into a coma, was indicted today on charges of second-degree murder, manslaughter and endangering the welfare of a child.

Her adoptive mother has been charged with second-degree murder for failing to report the abuse. She was not named in today's indictment.

In a city where murder and calamity provide routine grist for the tabloids, the death of Elizabeth Steinberg, a sandy-haired child called Lisa, has touched a deep nerve. Her sad face, photographed at the Halloween party at P.S. 41, stares out from the newspapers. Why, people here are asking, couldn't she have been saved?

Her adoptive father, Joel Barnet Steinberg, 46, is a successful New York criminal lawyer. His common-law wife, Hedda Nussbaum, 45, had been an editor at Random House and has written children's books. They live in a fashionable, five-story brownstone on West 10th Street.

But when police searched the apartment after Lisa was hospitalized, they found blood and feces on the wall. They found marijuana, cocaine, crack pipes, a scale to weigh drugs and $25,000 in cash. And they found the couple's other adopted child, 16-month-old Mitchell, tied to a chair, drinking spoiled milk and sitting in his own feces. He is being placed in foster care.

The intense coverage of Lisa's death might suggest that it is a rare occurrence. But officials say 102 children died of abuse in New York state last year, with 30 more deaths under investigation. Reports of abuse have nearly doubled, to 95,000, since 1981.

Nationally, callers reported suspected abuse of 2.2 million children last year; about 40 percent of such reports are substantiated. In the 34 states that collect mortality figures, 727 children died from abuse last year.

Many such deaths involve poor, minority children and receive scant attention. That the Steinbergs appeared to some to be "good, solid middle-class people makes it more shocking," said Andrea Savage, an assistant professor of social work at Hunter College. "With a middle-class family, people are less willing to suspect abuse and neglect."

Steinberg, who represented an alleged major cocaine dealer last month, is being held without bail at Rikers Island prison. Federal drug authorities also are investigating.

A weeping Nussbaum was arraigned Thursday in a Queens hospital bed. Her face, covered with purple bruises and framed by gray frizzy hair, barely resembles old photos of a smiling brunette. Her gangrenous right leg was elevated, and she was hooked to an intravenous tube.

"She looks like she went three rounds with Marvin Hagler," Deputy Police Inspector Robert R. Frankel said. "Her nose is concave. Her face is swollen. If she's not a battered woman, I don't know what a battered woman is."

But Nussbaum "categorically denied she was ever beaten," Frankel said. "She said she's clumsy and she fell."

Police visited the couple's apartment Oct. 6 after receiving an anonymous complaint. Steinberg refused to let the officers in, saying it was just "a little family argument," Frankel said.

"The police would not leave until they could eyeball Ms. Nussbaum, but they just saw a swollen lip," Frankel said. He said they briefly saw the two children but noticed "nothing unusual." Since charges were not pressed, he said, no arrest could be made.

Neighbors say they have called police dozens of times over the last decade after hearing fighting, shouts and curses from Apt. 3W. Police said they have a record of only one other call several years ago, when a beaten Nussbaum claimed that she had been mugged.

"We obviously knew what was going on," said Ene Riisna, an ABC television producer who lives in the adjoining brownstone. "We could see this woman's face was broken. We've all wondered, what more could we have done?"

Riisna said that Steinberg had ripped his sink out of the kitchen wall and that the landlord was trying to evict him. When Nussbaum ventured outside, Riisna said, she "looked like a ghost. She'd look away and wouldn't say hello."

But neighbors say Steinberg doted on Lisa, who always appeared well dressed until the last few months, when she was seen with dirty hair and messy clothes.

The city's Human Resources Administration sent social workers to the apartment in 1983 and 1984 but no evidence of abuse was found. "Everything that was done was done appropriately," agency spokeswoman Suzanne Trazoff said. "That's a very hard thing for anyone to understand when you say the case was handled appropriately, and here we have a dead child."

The principal of P.S. 41, Elliot Koreman, told reporters that Lisa's teacher noticed her bruises one day but that Lisa blamed it on a fight with her brother.

"There were neighbors who saw the kid was bruised," Aaron H. Rosenthal, chief of Manhattan detectives, said. "A schoolteacher saw marks on her. They saw the deterioration . . . . Sometimes you're so anxious to get this baggage off your mind that you take the word of a 6-year-old who says her 16-month-old brother beat her."

Bernard Mecklowitz, a Manhattan school superintendent, said the schools need more trained guidance counselors "to look for the child who's withdrawn, overactive, who's unkempt or dirty, who looks like he or she has bruises. You don't have to be a bloody genius to figure out there's something wrong."

Meanwhile, investigators have turned up no record that Lisa was adopted legally. By not filing adoption papers, Steinberg avoided a court-supervised examination of his fitness as a parent.

David Verplank, a Long Island lawyer, arranged the adoption of the other child, Mitchell. Verplank said that he helped the 17-year-old natural mother put Mitchell up for adoption as a newborn, but that Steinberg did not file the necessary court papers after picking the baby up at the hospital.

"I knew he was an attorney and his wife an editor at Random House," Verplank said. " . . . They seemed to me the ideal placement."

Steinberg, a burly six-footer, is a graduate of Fordham University and a former Air Force lieutenant who received his law degree from New York University in 1970.

Nussbaum, a Hunter College graduate, taught at city schools and served as Random House's senior editor of juvenile books before leaving in 1982 to raise Lisa.

"She was a quiet and thoughtful, reticent sort of person," said Janet Schulman, associate publisher at Random House. "Something terrible happened to her."

No funeral arrangements have been made for Lisa. Neighbors on West 10th Street have placed a candle and flowers on the front stoop to remember her.Special correspondent Marianne Yen contributed to this report.