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.

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.”