WASHINGTON — The Justice Department has decided not to charge David Petraeus’s mistress, Paula Broadwell, with cyberstalking as part of its investigation into an e-mail scandal that led to the resignation of the CIA director and storied general.

Broadwell’s lawyer, Robert Muse, received a letter from US Attorney Robert O’Neill that said no federal charges will be brought in Florida related to ‘‘alleged acts of cyberstalking.’’