Trump's wife, Vanessa, went to the hospital complaining of nausea after opening the letter.
The newspaper's managing editor fostered a culture of fear and silence, current and former staffers said.
Trump won't like his hometown newspaper's take on the speech.
The editor in charge of the paper's Sunday edition was also suspended.
Managing editor Rob Moore told staffers he would get rid of people who complained about his behavior, sources said.
News of the investigation comes the same week NPR reported that parent company Tronc had launched an investigation into the newspaper's managing editor.
Four women accused Vereen of sexual misconduct ranging from harassment to assault.
The Vermont senator swore in Bill de Blasio for his second term on Monday.
The 23-year-old had appeared in hundreds of films.