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Senator Bernie Sanders is making significant inroads against Hillary Rodham Clinton in New Hampshire, with a new poll showing him in a statistical tie with Mrs. Clinton in the state.

A new survey released by Franklin Pierce University and The Boston Herald found that 44 percent of Democrats in the state are backing Mr. Sanders compared with 37 percent for Mrs. Clinton, a difference that is within the poll’s margin of error.

The last Democratic poll from the group in March showed Mr. Sanders with support of 8 percent of likely voters, demonstrating a significant erosion in the former secretary of state’s lead.

The Franklin Pierce survey follows a WMUR poll last week that also showed Mr. Sanders and Mrs. Clinton in a tight race in New Hampshire. Mrs. Clinton continues to poll well nationally, but questions about her use of a private email account and growing criticism from Republicans have taken a toll on her popularity.

Despite Mr. Sanders’s strength in New Hampshire, nearly two-thirds of Democrats in the state think Mrs. Clinton will ultimately secure the nomination. However, the lack of excitement for her campaign was illustrated by the fact that 51 percent said they could back her but that they were not enthusiastic about her candidacy.

As for Mr. Sanders, enthusiasm for the Vermont senator’s campaign is robust but voters have doubts about his electability.

Other Democratic candidates such as Lincoln Chafee, Martin O’Malley and Jim Webb are failing to gain much traction so far in New Hampshire, but voters to appear to have an appetite for another candidate to join the fray: Vice President Joseph R. Biden Jr. Of the 442 likely voters surveyed, 46 percent said Mr. Biden should run for president.