A growing chorus of critics has challenged Mayor Michael Bloomberg’s approach to fighting crime, pushing back against policies that he credits for making New York the safest major city in America.

With a few months left in office, Bloomberg can say crime fell 34 percent over a decade during his tenure. For much of his first two terms, he also was heralded as a healer for the city’s tense race relations.

But with Bloomberg’s third and final four-year term ending on January 1, Democrats seeking to replace him have joined civil rights leaders and the heavily Democratic city council in hammering at a cornerstone of his legacy: The New York Police Department’s crime-fighting tactic known as stop-and-frisk.

Critics say police randomly and unfairly stop young African American and Latino men, most of whom are never charged with crimes after being subjected to searches. But polls show that about half of New Yorkers support stop-and-frisk as a strategy that has helped reduce crime.

This week, the city council defied Bloomberg on the police power issue, approving a pair of measures on Thursday that he vigorously opposed. One creates an independent inspector general to monitor the NYPD, and the other expands the definition of racial profiling and allows people who believe they have been profiled to sue police in state court.

Both measures passed with at least the two-thirds majority needed to override his promised veto.

The defeat was unusual for Bloomberg, 71, a politically independent billionaire who rose to national prominence during more than 11 years in office. Through most of his tenure, Bloomberg has been feared and respected, enhancing his stature with a national coalition Mayors Against Illegal Guns and flirting with a presidential run in 2008.

“For two terms, it didn’t percolate so hot, this issue,” said Eugene O’Donnell, a professor at John Jay College of Criminal Justice. He said the public’s fatigue with Bloomberg and an overall skepticism about police work helped give an opening to some of the more intense critiques of stop-and-frisk.

“It appears there may have been a shift in opinion about policing,” O’Donnell said.

A Bloomberg spokesman noted that polling has showed strong public support for Kelly and the NYPD.

PUBLIC OPINION DIVIDED

In heavily Democratic New York City, the winner of the September 10 Democratic primary will be heavily favored against the Republican in the November 5 general election.

All five of the major Democratic candidates have called the number of stop-and-frisk incidents excessive. Only City Council Speaker Christine Quinn, a Bloomberg ally, has said she would keep Police Commissioner Ray Kelly, who has described stop-and-frisk as an invaluable crime-fighting tool, though she said she would demand a drop in the number of stop-and-frisk incidents.

One turning point in the perception about Bloomberg may have come last May, when the New York Civil Liberties Union (NYCLU) released statistics showing police conducted more stops of black males between the ages of 14 and 24 than the total number of young black males living in New York City.

Police stops surged from 160,851 in 2003 to 685,724 in 2011, when 1.8 percent of searches of minority suspects that year resulted in weapons seizures.

At a news conference this week, Bloomberg invoked the high-crime days of the 1970s in a strong warning to council members not to pass the bill.

Bloomberg and Kelly have also irked advocates and members of the city council by invoking the names of al Qaeda and violent street gangs to make their case.

“What they’re doing is preying on people’s fears. Everyone wants to live in a safer city,” said Donna Lieberman, executive director of the NYCLU.

On Friday, Bloomberg appeared to double down.

“And you know, everybody’ll say, ‘Oh, you’re overstating it.’ I don’t know if you’re overstating it or not, but I’m not willing to find out,” Bloomberg told a radio program. “I don’t know what you’d say at the eulogy if a cop got killed, and say, ‘Well it turned out we weren’t overstating it. Sorry.”

The public’s view of the debate is mixed.

A Marist poll released on Thursday found New Yorkers were happy with Kelly – more than half want him to continue in the next administration – and about half said the practice of stop-and-frisk should continue. But just 6 percent of voters thought crime should top the next mayor’s agenda.

“It’s been some time since crime has been at the top of minds,” said Lee Miringoff, director of the Marist Institute for Public Opinion.

A Marist poll from the high-crime days of 1992 found that 33 percent of New Yorkers saw crime as the top issue