The next time Hillary Rodham Clinton visits New Hampshire, she need not look over her shoulder to find Bernie Sanders; the Vermont Senator is running right alongside her in a statistical dead heat for the 2016 Democratic presidential nomination, according to a CNN/WMUR poll released on Thursday.

The poll shows Mrs. Clinton drawing 43 percent of likely Democratic primary voters compared to 35 percent for Mr. Sanders, but with a margin of sampling error of plus or minus five percentage points, the race is a statistical tie.

While Mrs. Clinton has been enormously popular in New Hampshire, her favorable ratings have dropped almost 20 points since February, while Mr. Sanders’s have been climbing. And his negatives are lower than hers. So their net favorability ratings (favorable minus unfavorable) are now equal, at 55 percent.

In her favor, however, is that most voters appear to view Mrs. Clinton as by far the stronger leader, and as having the personal characteristics that are most presidential. She also trounces Mr. Sanders on her perceived ability to handle important issues, with more voters saying she is best able to handle the economy, terrorism, trade and health care.

Working against her is the hefty 28 percent who view her as the “least honest.”

Working to Mr. Sanders’s advantage: Most voters believe he “best represents Democrats like yourself” and “cares the most about people like you.” The one issue that voters said he was better able to handle than Mrs. Clinton was dealing with “big banks and corporations.”

The poll, conducted by the University of New Hampshire, interviewed 1,010 voters from June 18 to 24. The margin of sampling error for the entire poll was plus or minus three percentage points, but for the 360 likely Democratic primary voters who were interviewed, it was plus or minus five percentage points.

A Suffolk University poll last week also found Mr. Sanders making headway against Mrs. Clinton, trailing her by 10 percentage points, just outside that poll’s margin of sampling error of plus or minus four percentage points.