If the New York Police Department had a model of a polite policeman, it might be Paul Daly, now in his 16th year on foot patrol in Times Square. “ ‘The Color Purple’? Eight blocks north,” he called out the other day, directing a warm smile toward a woman who appeared lost.

She glared back.

“People ask for help, then they argue,” Officer Daly said with a laugh. It was impossible to tell what had offended the woman. Officer Daly’s tone of voice? His demeanor? His uniform? Whatever it was, she went away unhappy.

For most people, direct encounters with the police are rare occurrences. The vast majority of New Yorkers will never be arrested, and the vast majority of officers will never draw their guns.

But when passing encounters with the police go wrong, they can leave a lasting impression and can do as much damage over time to police-public relations as a highly publicized case of police brutality.

A decade after adopting the motto “Courtesy, Professionalism, Respect” and holding precinct commanders accountable for civilian complaints, allegations of discourtesy by the police are on the rise: up 47 percent in five years, to 3,807 in 2006.

And so the department has started a new effort to make sure officers are, quite simply, more polite. It includes role playing — at one recent session, cadets had to deal with actors playing out an interracial dispute, and a transgender robbery victim who was becoming hysterical — and one new but simple tactic: officers are going to start introducing themselves to people on the street.

“No matter what the encounter, from just saying hello on the street to an enforcement situation, we want them to know that the way they conduct themselves is critically important,” said Deputy Chief George W. Anderson, commanding officer of the Police Academy, where the training began in June with a panel discussion by civil libertarians and role playing sessions designed to test the composure of 1,100 cadets.

The officers will be saying hello during their first six months on the job. While on patrol, they must approach people, introduce themselves to merchants and others whom they see regularly and keep a record of such encounters in their memo books that can be checked by their commanders.

Recent rudeness complaints against officers range from the seemingly minor, like an officer’s refusing to give his badge number when asked, to more serious, like an officer’s telling some subway riders to “Learn English or go home.”

The new initiative has raised an interesting question with some law enforcement experts: Do good manners translate into good policing? Some disagree with the politeness plan, saying sometimes police officers, frankly, have to be mean or rude to get their jobs done.

“Whether people want to acknowledge it or not, policing is a contact sport,” said Maki Haberfeld, chairwoman of the Department of Law, Police Science and Criminal Justice Administration at John Jay College of Criminal Justice. Being polite “is not relevant,” she added.

A succession of mayors and police commissioners have crafted initiatives aimed at improving community relations, usually coinciding with a public outcry over police brutality. They have met with mixed success.

In 1997, with the police torture of Abner Louima in the headlines, then Mayor Rudolph W. Giuliani ordered every officer in the department to attend discussion groups with a panel of civil libertarians and law enforcement experts.

In 2001, with memories of the fatal police shooting of Amadou Diallo in 1999 still lingering, then Police Commissioner Bernard B. Kerik proposed — but never put in place — a sweeping plan to send commanding officers to community meetings and make precinct houses more welcoming by assigning officers as greeters and installing electronic information kiosks.

Still critics say the sense of antipathy is highly charged among minorities and the poor.

“The issue that contributes most to the gut level animosity between the police and the community is courtesy,” said Dennis deLeon, president of the Latino Commission on AIDS and a member of the Civilian Complaint Review Board. The board handles reports of discourtesy, foul language, excessive use of force and abuse of authority by police officers.

“When you get into black and Hispanic communities, an ‘us and them’ mentality takes over, and things get said when no one else is around,” he said. “It is hard for me to see any improvement.”

For the police on the street, technology has heightened the pressure: The city’s 311 telephone system has provided an easy outlet to people to complain, and the widespread use of cellphone cameras and personal recording devices makes any officer who steps out of line vulnerable to having his slip recorded for posterity.

Professor Haberfeld said oversight by civilian observers and the department had made officers shy away from time-tested tactics in handling some volatile confrontations. Normally, officers adhere to a “continuum of force,” she said, which dictates that they resort to using physical constraints or their weapons only after trying to engage a suspect in conversation.

“Some situations dictate that you skip the pleasantries,” she said. “Isn’t it better to raise your voice or use a nasty word than to put on the handcuffs?”

Whether the police have become more courteous, particularly when there is no threat of violence, is unclear. The records of the Civilian Complaint Review Board suggest that the public has been complaining more about police language and manners, but that more complaints might not mean more misconduct.

In five years, the records show, the number of allegations of police misconduct have soared by 91 percent, to 25,452 in 2006.

Andrew Case, a spokesman for the board, which employs 146 civilian investigators, said the increase had resulted in part from the convenience people find in using 311 to vent their annoyance over an unwanted police encounter, and from a spike in “stop and frisk” operations by the police, which have prompted many complaints that people were stopped on insufficient grounds.

Police courtesy is most directly reflected in allegations that the police used curse words, rude gestures or other forms of discourtesy, which increased 47 percent in the same five-year period, to 3,807 in 2006. More serious allegations of the police using ethnic, racial, religious or sexual slurs rose 84 percent, to 662 in 2006.

But the number of complaints that were substantiated may tell a different story.

In one example, the records show that while the number of complaints about serious slurs rose sharply, the number that were substantiated by the board’s staff fell.

Although more than 350 complaints were made during each year from 2002-6, fewer than 25 were substantiated in any of those years, and only 3 were substantiated in 2006, despite what Mr. Case said were vigorous investigations.

Officers found to have violated the discourtesy rules usually receive reprimands and negative notes in their personnel files. For the more serious use of offensive slurs, they are also docked vacation days. Substantiated complaints also can stand in the way of promotions.

In one severe case of offensive language, an officer was penalized with the loss of 17 vacation days last year after an encounter with a 17-year-old girl who dropped a chicken bone on the sidewalk, and complained when the officer said he was writing her a summons for littering.

The officer was found to have strung together a verbal assault that included a curse word and a racial epithet, and made matters worse by telling the girl and her companions, all of them black, “that’s how y’all think.”

Mr. Case said a recent allegation of offensive language had been made against an officer who was working in the subway and was reported to have responded, “you should learn English or go home,” when someone suggested subway signs be provided in several languages.

Complaints of discourtesy have been lodged against other officers who were said to have refused to provide their names and shield numbers to civilians who asked for them, he said, and who simply refused to respond when they were asked for directions.

For an officer on the street, keeping composure is not always easy. Few people, experts said, are routinely in situations where they face the brunt of other people’s anger like an officer trying to intercede in a family dispute, or calm someone who has been attacked.

“Sometimes you can’t believe the things people say to you out here,” Officer Daly said. “Schoolteachers would not listen to it, and you certainly wouldn’t take it from your kids, but people are always watching how a cop is going to react.”

At the Police Academy, instructors and professional actors staged encounters in which cadets participated, but were given no warning about how to react. A Chinese couple who spoke only Mandarin acted out a family dispute, black and white actors played out a racial dispute in a restaurant, and a man played a transgender robbery victim who was becoming hysterical.

Chief Anderson said the cadets were trained that the right response was not always polite conversation.

“The situation may preclude social niceties,” he said. “But the need to be authoritative, or to be commanding, doesn’t translate into every encounter they have with the public.”