Being the front-runner in a race for mayor of New York City often comes with exceptional scrutiny. But few have presented their opponents with quite as many targets as former Gov. Andrew M. Cuomo.

In the weeks since Mr. Cuomo joined a crowded Democratic primary field and immediately catapulted to its front, a group of New Yorkers whose relatives were nursing home residents who died of Covid have repeatedly blamed him for their suffering.

Women’s groups have picketed his campaign events to remind voters of the sexual harassment accusations that drove him from the governor’s office.

Then, on Thursday, years-old sworn testimony surfaced in The New York Post describing Mr. Cuomo and his longtime top aide, Melissa DeRosa, as having been in an “emotionally intimate” relationship.

Mr. Cuomo’s proximity to Ms. DeRosa would seem to have little bearing on his qualifications to be mayor. But the sudden re-emergence of the long-denied rumors underscored how his tenure as governor left Mr. Cuomo with a lengthy list of enemies and political baggage ripe for attack.

For now, Mr. Cuomo has maintained a comfortable polling lead against nine Democratic challengers, including Mayor Eric Adams. Yet as New York City political history has long demonstrated, a perceived lead comes with real risks — especially months before Primary Day.

“When you’re the only game in town, you’re the only person to take down,” said Mike Morey, the campaign spokesman for then-Council Speaker Christine Quinn in 2013, who watched her early polling lead in that year’s mayor’s race collapse. “You’d probably rather be second or third place and just climbing.”

New York City lets voters rank up to five candidates in order of preference on their primary ballots. Opponents of Mr. Cuomo and Mr. Adams are trying to stop their ascent by popularizing the acronym D.R.E.A.M., or “Don’t Rank Eric or Andrew for Mayor.”

Mr. Cuomo’s result may well be different than Ms. Quinn’s. He is better known and more battle-tested than almost any of his predecessors. His allies believe that that he can prevail as long as he can redirect voters’ attention toward his record of accomplishment during roughly a decade as governor, during which New York State legalized same-sex marriage, raised the minimum wage and rebuilt LaGuardia Airport.

“New Yorkers know the city is in crisis and Governor Cuomo is the only candidate in this race with the experience and the record of results to help fix it and make it a safer and more affordable place for all,” said Rich Azzopardi, Mr. Cuomo’s spokesman. “This is why these petty attacks are falling on deaf ears.”

But as Mr. Cuomo’s opponents are eager to point out, his tenure in Albany was also marked by turmoil, controversy and heavy-handed tactics that have left him with higher unfavorable ratings in recent polls than any candidate except Mr. Adams.

“The fly in the ointment is that he’s not particularly lovable,” said Mark Green, who narrowly won the 2001 Democratic primary for mayor, only to lose in the general election to Michael R. Bloomberg.

Those trying to stop Mr. Cuomo have been far more vivid. On Sunday, nine mayoral candidates gathered in Brooklyn alongside relatives of nursing home residents who died of Covid-related complications during Mr. Cuomo’s governorship. They hammered him for his policy directing nursing homes to admit hospital patients who had tested positive for the coronavirus.

“Could any other issue bring us all together with the differences that we have?” said Curtis Sliwa, the Republican candidate for mayor. “No — it’s the death, the unneeded death, of all these folks who were trusting the governor to do the right thing.”

Mr. Cuomo has said the state’s public health policies, including those involving nursing homes, adhered to federal guidelines, and he has accused federal authorities of trying to scapegoat him politically.

That controversy was largely eclipsed by accusations, including from former state employees, that Mr. Cuomo had sexually harassed them. The claims prompted an investigation by the office of the New York attorney general, who concluded in August 2021 that Mr. Cuomo had harassed 11 women.

He resigned within days of the report’s release, though in the years since, he has spent millions of dollars in legal fees fighting to clear his name. He denies any wrongdoing.

It was in March of that year, around the time that Mr. Cuomo was facing the first of those accusations, that The Daily Mail approached the governor’s office with questions about his relationship with Ms. DeRosa. It was preparing to publish photographs that showed the pair seated close together, huddled in conversation over drinks at a Manhattan restaurant.

Ms. DeRosa was also concerned that the outlet would publish longstanding rumors that she and Mr. Cuomo were more than just colleagues. She called Josh Vlasto, who had previously served as Mr. Cuomo’s chief of staff and who was an informal adviser, for advice on dealing with the publication, according to Mr. Vlasto’s testimony during the sexual harassment investigation.

In the transcript of that testimony, Mr. Vlasto is quoted as saying that Ms. DeRosa, who was married at the time, told him she did have an “emotional romantic relationship with the governor,” but said that the two had never been sexually involved.

“Emotionally intimate was the words she used,” Mr. Vlasto said. “I didn’t press on what that meant.”

The former governor’s younger brother, Chris Cuomo, was also brought in to brainstorm a response, according to Mr. Vlasto’s account. “He had said do you intend to be together in the long-term or do you intend to be together after you’re in office,” Mr. Vlasto said of Chris Cuomo. “She said I don’t know.”

The trio agreed that Ms. DeRosa would deny a romantic relationship to The Daily Mail; Ms. DeRosa ultimately told the publication that she and the governor “never had an intimate relationship.”

Mr. Vlasto testified that after The Daily Mail published the photographs, Ms. DeRosa told him that she had not had a romantic relationship with Mr. Cuomo, contradicting her earlier account.

Months later, in her own testimony in the sexual harassment investigation, Ms. DeRosa also denied having had a romantic relationship with Mr. Cuomo.

Investigators separately asked Mr. Cuomo whether he had had any romantic relationships with members of his staff.

“Never,” he said.

On Thursday, after The Post published its article, both Catherine M. Foti, a lawyer for Ms. DeRosa, and Mr. Azzopardi reiterated that there had been no physical relationship between Mr. Cuomo and Ms. DeRosa.

“Of course after seven years of working together for New York, the governor and Melissa were emotionally close,” Mr. Azzopardi said. “We all were after going through Covid and everything else together.”

Mr. Vlasto declined to comment.

The interview with Mr. Vlasto took place in the summer of 2021, but Mr. Vlasto’s account of Ms. DeRosa’s request was not reported before Thursday.

The transcript of his testimony posted on the attorney general’s website is redacted, and it conceals Ms. DeRosa’s name and much of Mr. Vlasto’s remarks about her and Mr. Cuomo. But an unredacted version of the transcript was posted briefly in 2022 as part of a broader tranche of investigative materials, before it was taken down and replaced.

A spokeswoman for the attorney general, Letitia James, said the unredacted version had been posted by accident, and that it had only been up for two hours.

The New York Times was able to access the unredacted transcript of Mr. Vlasto’s testimony using The Internet Archive’s Wayback Machine, which preserves web pages.

Mr. Azzopardi, though, called for an investigation into how the unredacted transcript became public. In a statement, he accused Ms. James of using “lawfare” to harm Mr. Cuomo and of helping to resurface the transcript as part of a “transparent ploy” to aid one of his rivals in the mayor’s race, Adrienne Adams, the City Council speaker.

The spokeswoman for Ms. James declined to comment on the accusation.