Robert F. Kennedy Jr. took the witness stand in Albany on Tuesday in his fight to keep his place on the New York ballot, a case that opponents believe could lay the groundwork for challenges of his candidacy in other states.

Mr. Kennedy, whose independent presidential campaign has found a small but potentially critical slice of supporters, has been challenged in a lawsuit in New York brought by voters who say that he used a false address on nominating petitions.

They say that address — in Katonah, N.Y. — is not his residence, but that of a friend, and thus the signatures on Mr. Kennedy’s petitions are invalid. A decision to knock the candidate off the ballot in New York would be likely to lead to lawsuits in other states where his campaign used that address information to gather signatures.

With a confession of a bear-dumping prank a decade ago still drawing criticism from public officials and late-night mockery, Mr. Kennedy has taken two days off the campaign trail to contest the suit in State Supreme Court. He swore under oath on Tuesday that he lived in Katonah, a Westchester County town about an hour north of midtown Manhattan.

He said that he didn’t feel that those that had signed his petitions had been misled.

“I think they were signing up to support me,” he said, adding, “I think most of these people did not care” about the address.

On Sunday, Mr. Kennedy made a jarring admission that he had gathered up a dead cub he found alongside an upstate highway in 2014 and then dumped the carcass in Central Park.