Amy Bernstein, a traffic court judge in Brooklyn, was heading home from work one night in late April when, she said, a young man carrying a clipboard approached her on the subway platform, asking if she would sign a petition to help place independents on the ballot in New York.

The top of the petition was folded underneath itself, so that the names of the candidates were not visible, Ms. Bernstein said. She asked for more details and told the man she was a judge — at which point he yanked the clipboard away, she said, and asked: “Am I going to get in trouble?”

The petition was for Robert F. Kennedy Jr.’s independent presidential campaign, which is working to collect the signatures needed to secure a spot for him on the November ballot in New York State. The campaign needs 45,000 but is aiming for more than 100,000. Candidates often collect far more signatures than they need in case some end up being invalidated for various reasons.

“At a minimum, it’s misleading,” Ms. Bernstein said of the interaction. “I was just pretty much taken aback.”

More than a half-dozen New York City residents, including two who are journalists at The New York Times and were approached randomly, have described similar encounters with signature gatherers for Mr. Kennedy in Brooklyn over the past three weeks. In each case, the resident was approached by a clipboard-wielding petitioner and asked to support “independent” or “progressive” candidates, or, in one case, to help get Democrats and President Biden on the ballot.

In three cases, the petitioners said that they were being paid for the work, the people who were approached said; in four cases, the petitioners said they had been told by a supervisor not to show or mention Mr. Kennedy’s name. Descriptions and photographs of the petitioners suggest that they are at least four different people. The petitioners themselves could not be identified or reached for comment.

In each of the encounters described to The Times, the names of Mr. Kennedy and his running mate, Nicole Shanahan, were hidden by the paper being folded. Only the slate of electors — the little-known people designated to vote for the candidates in the Electoral College — was visible in fine print at the top.

Most of the New Yorkers who spoke with The Times have experience in law or politics, including two who have worked in Democratic politics. They all said they had found their encounter curious, which led them to post about it on social media or reach out to reporters. In two cases, they reported the matter to state officials.

Mr. Kennedy’s campaign manager, Amaryllis Fox Kennedy, who is also his daughter-in-law, said the described conduct was “utterly at odds with all of our intensive training and materials.” She said the campaign would take legal action against any paid contractor found to be engaging in such activities.

Ms. Kennedy said the campaign had a number of paid contractors in New York, who in turn tended to hire local crews, “who themselves often hire others.” She said the campaign would undertake a review of its gathered petitions “for any hint of folded paper,” adding that the campaign staff members responsible for routine fraud checks had not seen any sign of such activity.

“We take ballot access, voter rights and truthfulness extremely seriously around here,” Ms. Kennedy said. “It’s the very substance of what motivates us to fight the establishment parties in the first place.”

Slippery or misleading tactics are hardly novel in the world of signature-gathering to gain ballot access for political candidates. Campaigns often turn to outside firms — who in turn hire temporary workers — to perform the time-consuming, expensive work of stopping residents on the street. Mr. Kennedy needs to gather hundreds of thousands of signatures across the country as his campaign scrambles to get him on the ballot in all 50 states, relying on a sprawling network of volunteers, contractors, consultants and lawyers.

While some of the encounters described to The Times could be considered misleading yet legal, others could fall into the category of election fraud, legal experts said, or could at least be used as fodder for court challenges.

James A. Gardner, a professor at the University at Buffalo School of Law, said that even folding petitions to conceal the names of candidates probably amounted to fraud. “This is one of those strange instances where the law and common sense align,” Mr. Gardner said.

The whole point of gathering signatures, Mr. Gardner said, is to show that a base of qualified voters in the state want to vote for that candidate. “There is New York case law that invalidates petitions when the purpose of the petition has been fraudulently misrepresented.”

He pointed to a 1959 court ruling that arose from a case in Queens, in which a judge ruled that residents had been fraudulently induced to sign a petition supporting a slate of candidates for local office: The petitions had been folded to conceal their true purpose, and people were told they were signing onto school busing or tax proposals. The judge ruled that the candidates could not be placed on the ballot.

But Jeffrey M. Wice, a professor at New York Law School who specializes in elections and voting rights, said he was not sure if state law explicitly outlawed misleading petitions, or if folding down the sheets would count as altering them illegally.

“This really gets down to whether the Kennedy petitions are challenged down the road,” Mr. Wice said. “If they are, this could be brought to the court’s attention.”

Mr. Kennedy, 70, an environmental lawyer who in recent years has become a prominent vaccine skeptic and purveyor of conspiracy theories, is already on the ballot in California, Delaware, Hawaii, Utah and Michigan, a battleground state. His campaign says he has also gathered enough signatures in Idaho, Iowa, Nebraska, Nevada, New Hampshire, North Carolina and Ohio. Legal challenges are all but certain, as Democratic allies of Mr. Biden wage a fierce campaign to block Mr. Kennedy from state ballots.

New York is one of the least hospitable states for independent and third-party candidates, after the 2020 passage of a law that sharply limited automatic party ballot access and set up stringent rules for gathering signatures. Independent candidates have just six weeks to gather 45,000 verified signatures. Across the country, the process has long been ripe for misleading tactics, mistakes or fraud: Several Republican candidates for governor in Michigan were knocked off the ballot in 2022 because of forged signatures collected by outside petition companies.

The Kennedy campaign has hundreds of volunteers gathering signatures across New York State. A training document for these volunteers, which was viewed by The Times, gives clear instructions about how to gather petition signatures, starting with: “Do not misrepresent yourself or the petition in any way.”

The volunteers’ work has been supplemented with paid signature gatherers.

Jeffrey Norquist, a professor of sociology at Farmingdale State College, said he had been approached on the platform at the Atlantic Avenue-Barclays Center subway station, a heavily trafficked area and major transportation hub in Brooklyn, and was asked if he would sign a petition to get third-party candidates on the ballot.

“I am usually game for this sort of thing,” Dr. Norquist said. But he noticed that the top of the page had been folded, obscuring the candidates, and he asked why. The man said it was a petition for Mr. Kennedy, and Dr. Norquist walked away.

Two days later, he saw a man on the same platform — he could not say if it was the same one, “a late-20s basic white dude” — and Dr. Norquist asked him why he was ”deceiving” people. It did not matter, the man said, because Mr. Biden was going to win New York anyway. He said he was just looking to make a few dollars.

Joel S. Berg, who leads a hunger- and food-security nonprofit group, was out for a run on a Saturday in late April when he saw a man with a petition clipboard. A veteran of Democratic politics and petitioning efforts, Mr. Berg stopped. He recalled that the man said he was trying to help “Joe Biden and other Democrats,” and then murmured: “And Kennedy.”

Mr. Berg said that he asked the man if he was a paid canvasser, and that the man said he was. “I didn’t really want to bust his chops,” Mr. Berg said. “But if a campaign I liked did something deceptive, I would have been offended.”

Ira Pearlstein, a lawyer, said he had been approached twice on the sidewalk near Barclays Center in Brooklyn, right above the Atlantic Avenue subway station. The first time, he said, a man told him the petition was for “any candidate” to be placed on the ballot, but when Mr. Pearlstein unfolded it, he saw Mr. Kennedy’s name at the top.

“I told him this is very misleading, and very undemocratic,” Mr. Pearlstein recounted. The man, he said, responded that he would not bother him anymore.

The second time, Mr. Pearlstein said he was approached by a young man who said that he was a student, and that he hoped to make some money on the side. Mr. Pearlstein echoed his concern about the misleading petition. “It almost sounded like he didn’t quite know,” Mr. Pearlstein said.

Mr. Pearlstein said that his wife — who said she had been approached separately — had reported the matter to state election officials.

A spokeswoman for the New York State Board of Elections referred questions to the board’s division of election-law enforcement, which did not respond to a request for comment.

Ms. Bernstein, the judge, also reported her encounter to state officials. Then, standing on the subway platform last week, she felt a tap on the shoulder.

It was the same man, asking if she wanted to sign the same petition.

She answered with the most New York of questions: “Are you kidding me?”

Nick Corasaniti contributed reporting.