Former Secretary of State Hillary Rodham Clinton has a 3-point lead over Sen. Bernard Sanders in the early presidential state of New Hampshire, according to a new poll that shows Mrs. Clinton with a significant lead among Democrats but Mr. Sanders leading among non-Democrats planning to vote in the primary.

Mrs. Clinton was at 47 percent in the survey from the Democratic-leaning firm Public Policy Polling, with Mr. Sanders of Vermont at 44 percent and former Maryland Gov. Martin O’Malley at 3 percent.

Mrs. Clinton led Mr. Sanders by 19 points among Democrats, 55 percent to 36 percent, but Mr. Sanders had a 30-point, 59 percent to 29 percent, lead among non-Democrats planning to vote in the state’s primary.

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“Hillary Clinton and Bernie Sanders have been within 2 to 3 points of each other on our last two New Hampshire polls,” said Dean Debnam, president of Public Policy Polling. “Clinton is dominant with the Democratic establishment, but Sanders is proving to be more appealing to people outside the party. It may come down to how many of those non-Democrats he can get to come out and choose to vote in the Democratic race rather than the Republican one that’s drawn a lot more interest.”

Sixty-eight percent of Clinton backers said they were definitely committed to supporting her, compared to 62 percent of Sanders voters.

Mr. Sanders has a 2.5-point edge over Mrs. Clinton in the state in the latest RealClearPolitics average of recent polls.