The producers of that fluffy farce "The Muppets Take Manhattan" felt compelled to add a touch of authenticity to their portrait of New York: Miss Piggy was mugged in Central Park.

The picture was released months before the city became a focus of ghoulish fascination with the case of Bernhard Hugo Goetz, who, having been assaulted in 1981, has confessed to shooting four youths who approached him on the subway last month. But it captured the popular perception of New York as the Wild West of American cities, a jungle of urban crime.

Only last week, someone moved a 100-foot crane onto a block of 44th Street after dark and tore down two low-income hotels -- without a city permit and without disconnecting the gas and water lines. The city was about to impose a moratorium on the conversion of such hotels to luxury housing.

Last Friday, the city transportation department reported that robbers were even stealing the streets: Hundreds of paving stones along the Henry Hudson Parkway were reported missing. Two men were arrested while prying up stones at 161st Street and Jerome Avenue in the Bronx.

A New York Times poll found that 49 percent of New Yorkers believe crime is the city's worst problem. The runner-up, housing, was cited by 15 percent.

According to the numbers, however, things aren't so bad. "What's all this dumping on New York?" asks ever-combative Mayor Edward I. Koch. "If you look at the crime statistics, Washington is worse than New York. But whenever something happens in New York, everybody is titillated."

New York ranks 10th in serious crimes per 100,000 citizens, according to statistics given to the Federal Bureau of Investigation. Detroit has the highest crime rate, followed by Boston, Dallas, Seattle, Denver, Los Angeles, Houston, Chicago and the District of Columbia. Then comes New York.

"If you've just been mugged, it's no comfort to say that statistically it is better here , but statistically it is better," said Manhattan District Attorney Robert Morgenthau, noting that serious crimes have dropped 17 percent since they peaked in 1981.

In the last few years, the city, recovering from a fiscal crisis, has beefed up its police force. Moreover, Morgenthau said, "We've put a lot of highly active criminals in prison."

Despite the statistics, however, "New Yorkers feel uncomfortable and threatened," said Dick Netzer, head of New York University's Urban Reasearch Center. "One of the things that is so maddening about New York is how uncivil so much public behavior is. Much of what sets the tone are things that seem trivial, like subway graffiti. Farebeaters. Kids playing loud radios and smoking on the subways. Littering . . . . There's a sense of lawlessness, of 'anything goes.'

"The Goetz case is the confirmation: The kids [who were shot] were boisterous. He didn't differentiate between the violence he had experienced earlier and the uncivil behavior. Both were threatening."

Like Goetz, who complained that his 1981 attacker was released in 2 1/2 hours (though he later served four months in prison), New Yorkers are incensed about the disarray in Manhattan's criminal courts.

"People are upset about the criminal justice system," Koch said. "It has broken down. You don't have speedy trials or the expectation of punishment."

The city-wide criminal court system is "in its death throes," according to a New York Bar Association report. Judges handle an average of 10 cases an hour -- one every six minutes. Only .5 percent of the cases go to trial as a result of crowded calendars and chaotic conditions, according to criminal attorneys.

"We need 20 more judges, and the legislature hasn't given them to us," Koch said. "You need individual calendars for judges so they will be responsible. The average case today has 17 adjournments."

While the statistics show less crime here than elsewhere, often the crimes, played up in the headlines of battling tabloids, seem more brazen: the jealous husband accused of murdering eight children and two women in last year's Palm Sunday massacre in Brooklyn; the "Mayflower Madam" who advertised her alleged call-girl operations in the Yellow Pages and posed for the cover of New York magazine after her arrest.

Francis T. Murphy Jr., presiding justice of the appellate division of State Supreme Court, was so furious after months of looking out his window on Madison Square Park and watching 20 to 30 people sell drugs openly that he wrote to the New York Law Journal urging amateur photographers to take pictures of the street action. Later, in a press release, he complained that "criminals have taken the city."

So blatant is the citizenry's disregard of the rules that in many neighborhoods the city has replaced its "No Parking" signs with ones that read: "Don't Even Think of Parking Here."

In The New York Times' Metropolitan Diary, a compilation of reader contributions, Alan Rosenberg, a Manhattan psychiatrist, reported witnessing this incident at an 86th Street theater last week. Seven or eight boys, ages 11 and 12, wanted to get into an "R"-rated movie (where those under 17 must be accompanied by an adult). According to Rosenberg, they approached an elderly woman in line wearing "a little hat perched atop her silver hair, orthopedic shoes on her feet and a grandmotherly smile."

"Perkily, sweetly," she agreed to buy their tickets, he reported. Each gave her $5 and waited nearby. "When she finally reached the box office," he wrote, "the little lady said, 'One, please,' grabbed her ticket, stuffed the bills in her coat pocket and shot into the theater."