The leader in the N.Y.C. mayoral race decided to join in the debate he had earlier said he would skip. His supporters said they were standing firm.Eric Adams on Thursday vigorously fought off accusations that he has misled New York City voters about his residency, a daylong defense that included a last-minute decision to join four of his mayoral rivals in a debate that he had intended to skip.The day included his release of a year’s worth of E-ZPass statements, meant to prove that he was not regularly commuting from a home he co-owns in Fort Lee, N.J., and an appearance in South Brooklyn with transit workers who endorsed him, saying they did not care where he lived, slept or visited as long as he worked for their interests.It concluded with his surprise appearance at the debate, which he had said he would skip for a vigil honoring a 10-year-old killed in gun violence. But by Thursday morning, the brouhaha had grown to the point that, Mr. Adams said, his attendance at the vigil for Justin Wallace, the 10-year-old killed in a shooting in Queens over the weekend, would be “a painful distraction.”Mr. Adams, the Brooklyn borough president and a leading mayoral candidate, blamed his opponents for trying to “politicize” the vigil.But even after three days of scrutiny — including the unusual spectacle on Wednesday of reporters peering into the refrigerator and closets of a basement apartment in a building he owns in Brooklyn, where he said he lives — there was still not much clarity on whether voters should be worried about revelations reported in Politico New York of apparent discrepancies in his official residence and his reportable income as a landlord.The E-ZPass toll records revealed a smattering of trips to New Jersey, presumably to the apartment that he co-owns with his partner across the George Washington Bridge from Upper Manhattan. But there was nothing to cement rivals’ accusations that he was living there, or even visiting on a weekly basis.Questions also centered on Mr. Adams’s failure to report rental income on his federal tax returns; Mr. Adams has blamed his accountant, and said he would release amended returns, but did not provide them on Thursday.And even if Mr. Adams, the Brooklyn borough president, was not living in New Jersey, it appeared that he was spending overnights in Brooklyn Borough Hall — an oddity given that his position is largely ceremonial and would not seem to require extended overnight hours even with the added pressure of campaigning, as he has suggested.Indeed, if Mr. Adams did live in New Jersey, it would be unlikely to affect his eligibility to be mayor. State law only says that he has to be living in New York City on Election Day in November, according to the state Board of Elections.So the controversy about his residence and work habits, at least for now, comes down to a battle of perceptions. And it was a battle where Mr. Adams appeared so far to be holding his own.By Thursday afternoon, Mr. Adams seemed to be relishing the confrontation, cheerful and surrounded by steadfast supporters from the transit workers’ union.“A question came up, and I answered it,” he said as he trotted to his car after speaking to city bus drivers at a depot in southern Brooklyn. “I did it the New York way. I didn’t run from it. I confronted the problem head on, the same way I confronted bad guys as a police officer.”The divide that was emerging was between rivals and critics who saw the confusion as a sign that Adams was evasive and possibly ethically challenged, and supporters who saw the whole issue as ginned up by rivals to distract from his appeal to working-class New Yorkers.Was he sleeping in Brooklyn’s Borough Hall, or New Jersey, to evade taxes, while running as a lifelong public servant and dyed-in-the-wool New Yorker — at worst violating laws, at best displaying poor time management and disorganization that might not bode well for running the city?Or was his chaotic-seeming lifestyle something more ordinary and relatable, the eccentric habit of a man with a life devoted to work and politics and overflowing, like so many other people’s, with conflicting commitments to professional, personal and family life?The latter take was how Roberto Martinez, a bus driver and a former police officer, saw it. At the bus depot with fellow members of Transport Workers Union Local 100, he called the candidate “a New Yorker true and blue.”.css-1xzcza9{list-style-type:disc;padding-inline-start:1em;}.css-3btd0c{font-family:nyt-franklin,helvetica,arial,sans-serif;font-size:1rem;line-height:1.375rem;color:#333;margin-bottom:0.78125rem;}@media (min-width:740px){.css-3btd0c{font-size:1.0625rem;line-height:1.5rem;margin-bottom:0.9375rem;}}.css-3btd0c strong{font-weight:600;}.css-3btd0c em{font-style:italic;}.css-w739ur{margin:0 auto 5px;font-family:nyt-franklin,helvetica,arial,sans-serif;font-weight:700;font-size:1.125rem;line-height:1.3125rem;color:#121212;}#NYT_BELOW_MAIN_CONTENT_REGION .css-w739ur{font-family:nyt-cheltenham,georgia,’times new roman’,times,serif;font-weight:700;font-size:1.375rem;line-height:1.625rem;}@media (min-width:740px){#NYT_BELOW_MAIN_CONTENT_REGION .css-w739ur{font-size:1.6875rem;line-height:1.875rem;}}@media (min-width:740px){.css-w739ur{font-size:1.25rem;line-height:1.4375rem;}}.css-9s9ecg{margin-bottom:15px;}.css-uf1ume{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-box-pack:justify;-webkit-justify-content:space-between;-ms-flex-pack:justify;justify-content:space-between;}.css-wxi1cx{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-flex-direction:column;-ms-flex-direction:column;flex-direction:column;-webkit-align-self:flex-end;-ms-flex-item-align:end;align-self:flex-end;}.css-12vbvwq{background-color:white;border:1px solid #e2e2e2;width:calc(100% – 40px);max-width:600px;margin:1.5rem auto 1.9rem;padding:15px;box-sizing:border-box;}@media (min-width:740px){.css-12vbvwq{padding:20px;width:100%;}}.css-12vbvwq:focus{outline:1px solid #e2e2e2;}#NYT_BELOW_MAIN_CONTENT_REGION .css-12vbvwq{border:none;padding:10px 0 0;border-top:2px solid #121212;}.css-12vbvwq[data-truncated] .css-rdoyk0{-webkit-transform:rotate(0deg);-ms-transform:rotate(0deg);transform:rotate(0deg);}.css-12vbvwq[data-truncated] .css-eb027h{max-height:300px;overflow:hidden;-webkit-transition:none;transition:none;}.css-12vbvwq[data-truncated] .css-5gimkt:after{content:’See more’;}.css-12vbvwq[data-truncated] .css-6mllg9{opacity:1;}.css-qjk116{margin:0 auto;overflow:hidden;}.css-qjk116 strong{font-weight:700;}.css-qjk116 em{font-style:italic;}.css-qjk116 a{color:#326891;-webkit-text-decoration:underline;text-decoration:underline;text-underline-offset:1px;-webkit-text-decoration-thickness:1px;text-decoration-thickness:1px;-webkit-text-decoration-color:#326891;text-decoration-color:#326891;}.css-qjk116 a:visited{color:#326891;-webkit-text-decoration-color:#326891;text-decoration-color:#326891;}.css-qjk116 a:hover{-webkit-text-decoration:none;text-decoration:none;}“It doesn’t matter,” he said of the residency question. “If you’re in Manhattan, you can see New Jersey. If that’s the best they’ve got, forget it. The president of the U.S. lives in Washington, D.C. That doesn’t mean he doesn’t represent the people in Washington, D.C., and the people in New Hampshire. If he wants to go spend the weekend in Jersey with his girlfriend, it’s not going to matter to me.”Election law experts said that the law was on Mr. Adams’s side.The state law governing residency states that “residence” means a “place where a person maintains a fixed, permanent and principal home and to which he, wherever temporarily located, always intends to return.”Courts have generally allowed candidates to have two residences, and they can select one as their “political home,” said Martin Connor, an election lawyer who was a state senator for 30 years until 2008.Mr. Connor, who is not working for any of the mayoral candidates, said courts have typically been generous with candidates, at times allowing people to claim a place as their residence even if they stay there only two nights a week. He said that Mr. Adams’ choice to stay with his girlfriend in New Jersey “doesn’t obviate his Brooklyn residence.”“Usually you’re OK if you got an apartment, you got a bed, you got a refrigerator, particularly if you own the building,” he said.Mayor Bill de Blasio also sided with Mr. Adams.“I’ve known Eric Adams for decades,” he said during his daily news briefing on Thursday. “He’s a Brooklynite. He’s a New Yorker. He’s served the city in many different capacities. I just don’t see an issue here.”Carl Murray, 65, of Manhattan, called controversies like this one “what I hate about politics,” adding, “You’ve got somebody doing something good, and you want to tarnish them.”“I mean, doctors live out of town,” Mr. Murray said. “Lawyers live out of town. Judges live out of town.”Mr. Murray said his criteria for a mayor are, “You come here, do your job, be on time.”Michael Rothfeld, Sean Piccoli and Dana Rubinstein contributed reporting. More