The Supreme Court said on Friday that it would not restore Robert F. Kennedy Jr. to the ballot in New York after a state court judge ruled that he had used a sham address on his nominating petition.

The court’s brief order gave no reasons, which is typical when it rules on emergency applications. No dissents were noted.

Mr. Kennedy has suspended his campaign and endorsed former President Donald J. Trump. But his lawyers told the justices that New Yorkers should be permitted to cast their votes for him. “A suspended campaign is not a terminated campaign,” they wrote.

Democrats have worked to keep third-party candidates off the ballot, viewing them as a threat to their ticket. In the past year, polling indicated that Mr. Kennedy would draw about the same number of votes from Mr. Trump and President Biden, while some more recent polls suggested that he would pull more voters from Mr. Trump than from Vice President Kamala Harris.

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Mr. Kennedy spends much of his time in a Los Angeles home he shares with his wife, the actress Cheryl Hines. But the petition listed an address in Katonah, a town in Westchester County. His lawyers told the Supreme Court that he rents a spare bedroom from a childhood friend there and “has stayed overnight on one occasion.”

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