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Edwards, 25, was off duty and in street clothes when he chased a man who had broken into his car.
Dunton and two other plainclothes officers patrolling nearby noticed the two men and ordered them to halt. When Edwards turned toward them with his gun out, Dunton shot him.
Because Edwards was black and Dunton is white, some civil rights advocates have charged that race was a factor in the shooting.
The Rev. Al Sharpton said Thursday that the decision was expected, as grand juries rarely indict officers in friendly fire shootings.
"We will continue to call on the governor to authorize a special prosecutor in this case," Sharpton said.
Edwards' mother, Natalia Harding, said in a television interview that she believed Dunton shot her son because he was black.
"I would like to see him go to jail," Harding said.
Dunton, 30, has been on administrative duty since the shooting.
He may still face an internal police department disciplinary review.
Police officials said the grand jury decision clears the way for an administrative review of the shooting to see if it fell within department guidelines for use of deadly force.
A spokesman for the police union said the union would have no comment.
According to the district attorney, Edwards was walking to his car in East Harlem and noticed the driver's-side window was broken. and a man was leaning inside rifling through items on the front seat. Edwards drew his gun and grabbed the man's shoulder with his left hand, Morgenthau said. A struggle ensued and the man ran. Edwards chased him, gun in hand.
Three officers in an unmarked car spotted the two men. They saw that the pursuer had a gun in his hand and pulled over.
According to the district attorney, Dunton got out of the car and yelled, "Police, don't move. Drop the gun. Drop the gun."
Edwards slowed but did not stop, turned and pointed his gun at Dunton, Morgenthau said.
Dunton fired six shots, mortally wounding Edwards. The man, later identified as Miguel Goitia, was arrested and charged in the case.
Emergency service officers arrived and tried to revive Edwards. It was only when they cut his sweatshirt open and saw his Police Academy T-shirt that they realized he was an officer.
Following the shooting, the NYPD revamped its training on confrontations with other officers.
In a statement Thursday, the department outlined several precautions ordered by Police Commissioner Raymond Kelly that seek to minimize the risk of friendly fire. They include hiring a psychology professor to study shooters' decision-making and surveying undercover officers for advice.
In addition, the NYPD is studying new technology that could avert friendly fire shootings. One early warning system would equip officers with devices that, once their guns are drawn, emit a signal to other officers in the area.
"I promise you we will do everything possible to learn from this tragedy," Mayor Michael Bloomberg told mourners at Edwards' funeral.
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