At a press conference held by Al Sharpton's National Action Network and Coppin's family at 4 p.m., a representative for the family disputed the police version of events, asking the public to wait for a fuller account of the incident.
"There is no credible evidence at this time that this was a suicide," the representative said when asked whether Coppin was seeking a suicide-by-cop.
"At some point in his life, he's had some mental distress but whether that affected his judgment, that remains to be seen."
Coppin had previously been incarcerated as a youthful offender and diagnosed with psychiatric problems, a source said, based on the review of a summary of a youthful offender report. To date, however, there is no indication that he had been treated since his release.
At least one neighbor reportedly challenged the police version of events. "I saw him put his hands out of the window, and then he got on top of the windowsill and sat down and jumped onto the street with his hands up and the brush in his hands," Andre Sanchez, 17, told the New York Post. "And that's when they shot him."
WABC-TV's Mark Crudele contributed to this report.