Not long after the official festivities ended, two men were fatally stabbed near the parade route, The New York Times reported Tuesday.
Earlier Monday evening a man and a woman were shot.
For the past nine years the West Indian American Day Parade has been marred by fatal shootings, the Times said.
Last year some police officers posted racial comments on Facebook about patrolling the parade while others were caught on video dancing suggestively with participants.
One Facebook poster called participants "savages" and "animals."
Seventeen officers were disciplined.
Police Commissioner Ray Kelly issued an apology to the West Indian American Day Carnival Association.