TORRINGTON, CONN. -- As Joanne Tremins was moving some belongings out of her ramshackle house on South Main Street two years ago, her 350-pound husband ran over, grabbed the family cat and strangled it in front of Tremins and her children.

For more than three years, Tremins said, she had complained to Torrington police about beatings and threats from her husband. Instead of arresting him, she said, the police acted "like marriage counselors."

The cat attack finally prompted police to arrest Jeffrey Tremins on a minor charge of cruelty to animals. But four days later, outside a local cafe, he repeatedly punched his wife in the face and smashed her against a wall, fracturing her nose and causing lacerations and contusions to her face and left arm.

That Joanne Tremins is suing this New England town of 34,000 is not without historical irony. For it was here that Tracey Thurman, now partially paralyzed from stab wounds inflicted by her husband, won a $2 million judgment in 1985 against the police department in a federal civil rights case that has revolutionized law enforcement attitudes toward domestic violence.

Attorney Burton Weinstein, who won the Thurman case and represents Tremins, said he is involved in 31 suits against police by battered women. "Some involve multiple abductions and rapes," he said. "Several involve killings that were broadcast in advance."

The Thurman case marked the first time that a battered woman was allowed to sue police in federal court for failing to protect her from her husband. The ruling held that such a failure amounts to sex discrimination and violates the 14th Amendment.

The resulting spate of lawsuits has prompted police departments nationwide to reexamine their longstanding reluctance to make arrests in domestic assault cases, particularly when the wife refuses to press charges. State and local lawmakers, facing soaring municipal insurance costs, are also taking notice.

The Connecticut legislature responded in 1986 with a law requiring arrests in domestic disputes if there is probable cause to believe that an assault occurred, regardless of whether the wife wants the arrest. New Jersey adopted a similar measure last month.

Such changes have had immediate impact. In the 12 months after Connecticut's law took effect, the number of family-violence arrests in the state increased 93 percent, from 12,400 to 23,830. In Newport News, Va., a new pro-arrest policy helped reduce the number of domestic homicides from nine in 1984 to three last year.

In New York City, family-violence arrests increased 67 percent in 1985 after police adopted a mandatory-arrest policy for felony assaults. The city acted after paying a $2 million judgment in a case in which police failed to stop a man, who had threatened his wife repeatedly, from attacking their infant daughter.

New York's law, because it leaves less severe attacks to the officer's discretion, was not strict enough to save the life of 6-year-old Lisa Steinberg, whose death last November sparked a public outcry.

Police responded to a complaint that her father, Greenwich Village attorney Joel Steinberg, was beating his wife, Hedda Nussbaum, but made no arrest when Nussbaum, despite obvious signs of injury, refused to press charges. Joel Steinberg was later charged with beating Lisa to death.

Here in hilly Torrington, the Thurman case has left similar scars. Police Chief Mahlon C. Sabo said it had a "devastating" effect on the town and his 70-member force.

"The police somehow, over the years, became the mediators," said Sabo, who took office last May. "There was a feeling that it's between husband and wife. In most cases, after the officer left, the wife usually got battered around for calling the police in the first place.

"I've had it happen to me as a policeman," Sabo said. "I remember going on calls where the phone had been ripped out of the wall, the wife had a bloody nose, a black eye, but she would not press charges.

"We were dealing with a societal problem we weren't trained to deal with. We were trained to shoot guns, to make arrests, not to be social workers."

Although the law now requires them to make arrests, police officers here said, the courts toss out many domestic cases for the same reason that long hampered police.

"Unfortunately, many women just want the case dropped and fail to recognize they're in a dangerous situation," said Anthony J. Salius, director of the family division of Connecticut Superior Court. "If she really doesn't want to prosecute, it's very difficut to have a trial because we don't have a witness."

Court statistics bear this out. Under Connecticut's 1986 law, authorities have prosecuted only one-third of those arrested in domestic assaults, with most drawing fines or suspended sentences. Charges have been dropped against the remaining two-thirds, sometimes in exchange for their participation in counseling, alcoholic treatment or other diversionary programs.

Until the late 19th century, much of the United States had laws allowing men to use physical force to discipline their wives. Among these was the infamous "rule of thumb," which allowed a husband to beat his wife provided he used a stick no thicker than his thumb.

Firm statistics are rare, and only in recent years has the scope of wife-battering drawn national attention. In 1986, according to the Federal Bureau of Investigation, 1,510 women were killed by their husbands or boyfriends.

In five New York precincts, counselors from the Victim Services Agency, a federally funded nonprofit group, join police in visiting families the day after a violent incident. Police Sgt. Joe Ryan said that 13,000 interviews have been conducted since mid-1985 and that about one-fourth of the families agree to further counseling.

Torrington police learn about domestic violence through videotaped role-playing sessions with local actors. In one version, they are confronted with a shouting husband and hysterical wife; in another, a gun-wielding man threatens police while keeping his wife in a hammerlock.

That training is one legacy of the graphic violence of the Thurman case. Nearly five years after the attack by her estranged husband, Tracey Thurman remains scarred and partially paralyzed from multiple stab wounds to the chest, neck and face. Charles Thurman was sentenced to 14 years in prison.

For eight months before the stabbing, Thurman repeatedly threatened his wife and their son, 2. He worked at Skee's Diner, a few blocks from police headquarters, and repeatedly boasted to policemen he was serving that he intended to kill his wife, according to the lawsuit.

In their defense, police said they arrested Thurman twice before the stabbing. The first charges were dropped, and a suspended sentence was imposed the second time. Tracey Thurman later obtained a court order barring her husband from harassing or assaulting her.

On June 10, 1983, Tracey Thurman called police and said her husband was menacing her. An officer did not arrive for 25 minutes and, although he found Charles Thurman holding a bloody knife, he delayed several minutes before making an arrest, giving Thurman enough time to kick his wife in the head repeatedly.

Less than a year after police were found liable in the attack on Thurman, Joanne Tremins also found that a restraining order obtained against her husband was worthless.

"I felt lost," she said. "There was no one in the world that could help me."

Sitting in her small kitchen, with a batch of color photographs showing her badly bruised from the 1986 beating, Tremins recounted how she made about 60 calls to police to complain about her husband, a cook. But she acknowledges that, on most of the occasions, when police asked if she wanted him arrested, she said no.

"How could I say that?" she asked. "He's threatening to kill me if I have him arrested. He's threatening to kill my kids if I have him arrested. He'd stand behind the cops and pound his fist into the palm of his hand."

Hours before Tremins strangled the cat on Feb. 11, 1986, according to the lawsuit, he beat and kicked his wife and her son, Stanley Andrews, 14. When an officer arrived, Joanne Tremins said, he told her that he could not make an arrest unless she filed a complaint at the police station.

"My son was all black and blue," Tremins said. "But {the officer} refused to come into my room and look at the blood all over the walls and the floor."

After Tremins was taken into custody for the cat incident, police did charge him with assaulting the son. He was released on bond, and his wife was issued a restraining order.

When her husband approached Tremins days later at a cafe in nearby Winsted, police refused to arrest him, despite the order. After the beating, Jeffrey Tremins was charged with assault and sentenced to two years in prison.

Sabo said Tremins' suit, which he called a "copycat" case, has numerous discrepancies. Sabo said that department records show fewer than half of the complaints to police claimed by Tremins and that she may have precipitated the violence by seeking out her husband. She denies this.

Torrington police, who have 110 restraining orders on file, said some women use them to harass their husbands or have them arrested, sometimes as evidence for a forthcoming divorce case. "It's their baseball bat," Capt. Alfred Columbia said.

Sabo said his biggest problem with the new arrest law is that police no longer can make distinctions between a shoving match and a savage beating. Even a minor, first-time altercation, he said, can result in arrest for husband and wife.

"You get handcuffed, taken out of your house in front of your kids, searched, locked up and the doors close behind you," Sabo said. "Now you've got an arrest record. We've labeled these people."

To attorney Weinstein, however, Torrington police are still dragging their feet. "That department has the gentlest learning curve I've ever seen," he said. "Indeed, it may be flat."