NEW YORK — New York City Mayor Bill de Blasio’s relationship with police, already strained by accusations he sided with frequent NYPD critic Al Sharpton over the chokehold death of an unarmed suspect, suffered another hit with revelations a top aide is living with a convicted killer who has often mocked officers as “pigs.”

Police unions say it’s only the latest incident that shows the Mayor’s lack of support for the 34,000-officer force. And even some de Blasio allies acknowledge the mayor could do a better job of leading the department he is simultaneously trying to reform.

“This is difficult terrain, particularly for a new mayor,” said Eugene O’Donnell, a professor of Police Studies at John Jay College of Criminal Justice who was on the Mayor’s transition team. “Morale has been low on the force and it’s only getting worse.”

Following a pair of mayors who were largely lockstep with the NYPD, de Blasio was viewed suspiciously by police from the beginning with his fierce push to end stop-and-frisk, the crime-fighting tactic that allowed officers to stop anyone they deemed suspicious but a judge ruled sometimes discriminated against minorities.

He drew their ire when he called a police official to inquire about the arrest of a political ally, who was later released. Police said the release had nothing to do with the mayor’s request but the unions said the call made it seem like de Blasio was undermining officers.

And the latest strain was the revelation that Rachel Noerdlinger, first lady Chirlane McCray’s chief of staff and a highly visible face at City Hall, is dating Hassaun McFarlan, who pleaded guilty to manslaughter in a 1993 shooting when he was 15 and later served time for drug trafficking.

The news website DNAinfo reported that McFarlan’s Facebook page, now taken down, had several posts referring to police as “pigs.” The city’s largest police union has called for Noerdlinger’s dismissal over the matter.

“It raises serious questions about her judgment and character and the quality of the counsel she provides to City Hall,” said union head Pat Lynch.

Although de Blasio defended Noerdlinger — “We don’t care what someone’s boyfriend says,” he said — the controversy shows no signs of abating.

It was revealed that Noerdlinger recently joined McCray for a high-level NYPD crime-fighting briefing while he city’s Department of Investigations opened an investigation into whether Noerdlinger failed to disclose that she lived with McFarlan. It later closed the investigation without recommending any disciplinary action.

But it’s de Blasio’s close ties to Sharpton — who is also Noerdlinger’s former boss — that has fueled much of the unions’ anger.

Sharpton spent months denouncing the NYPD for the death of Eric Garner, a black man who died from a police chokehold in July while being arrested for selling loose cigarettes on the street.

A Grand Jury convened to consider possible charges against the white officers involved and the entire police department is being put through use of force retraining.

In a City Hall summit called to ease tensions, de Blasio sat awkwardly between Police Commissioner William Bratton and Sharpton, who proceeded to rail against the NYPD, saying the mayor’s teenage son, who is black, could also be a “candidate for a chokehold.”

Police unions were outraged that Sharpton was given equal billing with Bratton. That became a central point in a full-page ad taken out by the Sergeant’s Benevolent Association in The New York Times opposing the city’s bid to host the 2016 Democratic National Convention.

“The mayor has provided a public platform to the loudest of the city’s anti-safety agitators,” wrote union president Ed Mullins. The ad also claimed that City Hall’s “diminished support for police officers translates directly into crime spikes and drops in quality of life.”

Mayoral aides strongly disputed any suggestion that de Blaiso’s leadership over the NYPD had been compromised. “The mayor has nothing but the strongest support for the brave men and women of the NYPD,” said spokesman Phil Walzak, who noted crime continues to fall.

But experts said there are political risks for de Blasio if the complaints grow louder.

“The perception that City Hall and the police are not on the same page does not usually sit well with voters,” said Costas Panagopoulos, political science professor at Fordham University.

De Blasio has repeatedly defended Bratton but the perception that Sharpton is given an outsized voice at City Hall has penetrated even the city’s elite, as evidenced by a roast at the annual white-tie Alfred E. Smith dinner Oct. 1st.

“What a crowd tonight,” Home Depot founder Kenneth Langone said, looking around the ballroom at the Waldorf-Astoria. “Although I don’t see the person in charge of the NYPD up here tonight, Al Sharpton.”

De Blasio, who was sitting nearby, smiled at the joke. And when the dinner ended, he hustled to a party for Sharpton’s 60th birthday, telling reporters “The more people criticize him, the more I want to hang out with him.”

(JONATHAN LEMIRE and COLLEEN LONG)