David Seastrand, 50, police chief of New London, near the state capital Concord, quit his job effective immediately under a deal with the office of state Attorney General Michael Delaney, prosecutors said.
Seastrand, who had been chief since 1995, also agreed to permanently give up his police officer's certification.
No charges will be brought against him in connection with the case, Associate Attorney General Jane Young told Reuters.
A call to an attorney for Seastrand was not immediately returned.
Delaney's office opened an investigation last month after the young woman accused Seastrand of telling her the charges would be dropped if she agreed to let him shoot nude photos of her.
The unnamed woman, a student at the private Colby-Sawyer College in New London, had been arrested on suspicion of underage drinking and giving a false name, according to her lawyer, Richard Lehmann.
Lehmann said the student would have liked to see Seastrand criminally prosecuted but respects the prosecutors' decision.
He said the "relatively minor charges" still stand.
"The ability for him to leave office and never be a police officer again was a very significant consideration," Young said.Copyright 2013 Thomson Reuters. Click for restrictions.