The San Francisco Police Officers Association, always a big player in the election of a new mayor, might find itself outside the arena this time around. The reason: None of the front-runner candidates matches its priorities.

“We may make an endorsement, we may not,” said the association’s former president, Gary Delagnes, who now works as a consultant for the union. Delagnes said he couldn’t remember a time in San Francisco’s recent history when the association has bowed out of a race.

But this year its 2,200 members are facing three top candidates in the June 5 election whose sharp public statements and legislative records have generated visceral mistrust within law enforcement.

•Acting Mayor London Breed, the race’s nominal moderate, jilted her allies on the police force when she voted for a day of tribute to Mario Woods, a stabbing suspect who was slain by police in the Bayview in 2015.

•Mark Leno, a former supervisor, state assemblyman and state senator, introduced an unsuccessful bill in Sacramento to open police personnel files when officers were accused of misconduct.

•Supervisor Jane Kim, a progressive, referred to police shootings as “government-funded murders” in a 2016 debate during her campaign for state Senate.

Former Supervisor Angela Alioto is a longtime friend of the police union, but she lags far behind the three front-runners in the race to fill out the term of the late Mayor Ed Lee, who died in December.

Police Officers Association President Martin Halloran declined to take a position on any candidate. He said the association will interview the candidates, probably in late February, and then its six-member legislative committee, which consists of police officers and union executives, will decide whom to endorse, if anyone.

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Support from law enforcement has long been key to winning citywide elections, said Democratic strategist Nathan Ballard, who is a spokesman for the Police Officers Association but stressed that he was not speaking on behalf of his client.

“To be mayor of the entire city, you need to win some votes west of Twin Peaks and the other moderate precincts of San Francisco,” Ballard said, noting that “public safety is a big issue on the west side of this city.”

Yet it’s unclear whether Breed, Leno, Kim or Alioto will earn that endorsement and its ancillary benefits. Among them: campaign money, volunteers to walk precincts and make phone calls, ads directed against opponents, and the prestige that comes with being associated with law enforcement, which could be especially potent with voters who are concerned about rising property crime.

Breed captivated Delagnes and other police officers during her 2012 district supervisor race. Painting herself as a girl from the projects who relied on the police to protect her from drug dealers and burglars, Breed was “a tremendous breath of fresh air,” Delagnes recalled.

“I loved her,” he said. “I was the No. 1 London Breed fan.”

But their relationship deteriorated after Breed settled into office and established herself as an outspoken critic of police violence during a series of fatal shootings involving San Francisco officers.

In July 2015 she called Delagnes, threatening an independent investigation into officers’ handling of Filimoni Raiyawa, who died after going into distress while in police custody. Officers had initially described Raiyawa as black, and police officials said Breed lost interest after hearing he was from Fiji.

Through her campaign consultant, Breed declined to comment on the Raiyawa situation.

The following year Breed championed the supervisors’ resolution to commemorate Woods. It passed unanimously, including support from Breed and Kim, prompting Delagnes to fulminate the next day on Facebook.

“This is, without a doubt, the most disgusting, idiotic and pathetic legislation I have ever seen in my 35 years of POA involvement,” he wrote.

Delagnes is still stewing. “The wounds are still very fresh on our side,” he said in a recent interview.

Police officers are also skeptical of Leno, who has long been an advocate for criminal justice reform and law enforcement transparency. In the 2008 state Senate race, the San Francisco POA poured $25,000 into an independent expenditure committee called Protect Our Kids, which sent out negative mailers and ran TV attack ads against Leno, some of which were perceived as homophobic.

“It was an ugly picture of him with a slogan that said something like, ‘Protect your children from Mark Leno,’” said Carole Mills, who was Leno’s field representative in Marin and Sonoma counties during that campaign. “They were implying that because he’s a gay man, he’s a pedophile.”

Delagnes, who was president of the association at the time, said he does not remember the ads.

“That would have been unfortunate,” he said.

In 2016, Leno angered police officers by introducing a bill that would have allowed public access to personnel records of officers accused of racial profiling, excessive force, sexual assault, making false statements or other serious offenses. It died in committee.

“It will certainly be a topic of conversation if or when we meet with Mark,” Delagnes said.

Jim Stearns, a consultant for Leno, downplayed the importance of police endorsements, saying the union’s influence has waned as voters veer toward “a more progressive criminal justice system.”

“Endorsements of organizations that are fighting for affordable housing, better public education, health care — these are equally if not more important endorsements for a candidate running for mayor,” Stearns said.

But it is Kim, who has consistently opposed Tasers and condemned police use of force, whom police revile most.

“I think it’s safe to say we will not be endorsing Jane Kim under any circumstances,” Delagnes said. He expressed doubt about Kim’s ability to tackle homelessness or reduce thefts and auto burglaries, three of the main issues that rile voters.

Kim’s campaign spokeswoman, Julie Edwards, pushed back on those comments. She said Kim will help police officers by investing in low- and moderate-income housing, so that police officers “can afford to live in the community they serve.”

The police have an amicable relationship with Alioto, who is also viewed as a moderate and who has taken a tough-on-crime stance. However, union leaders have privately expressed concerns about whether she can mount a viable campaign.

The police union is one part of the trinity of labor unions that normally ensures wins for moderate candidates, the others being the San Francisco Firefighters union and the Building Construction Trades Council.

So far, none of those unions has endorsed a candidate. Firefighters union President Tom O’Connor said his members like each of the top three — they appreciate Breed for demanding that Fire Chief Joanne Hayes White improve the city’s ambulance response times, Leno for his efforts in Sacramento to combat fire-related cancers and Kim for always seeming “to have an open ear.”

Michael Theriault, secretary-treasurer of the construction trades council, said he plans to hold back. His union is pitching two pieces of legislation dealing with building codes and labor protections to the Board of Supervisors, and its members are wary of making commitments in the meantime.

Further complicating matters, the police and firefighter unions are negotiating their first new contracts in 11 years, a process overseen by the mayor’s office. Those contracts have to be finalized and brought to Board of Supervisors by May 15, three weeks before the election.

If Breed remains acting mayor, her reputation could hinge partly on whether those negotiations lead to a good contract or fall apart.

Rachel Swan is a San Francisco Chronicle staff writer. Email: rswan@sfchronicle.com Twitter: @rachelswan