Police Chief Louis Algano called the student's death "a truly tragic situation," The Boston Globe reported Monday.
The Globe said Henry, 20, of Easton, Mass., was behind the wheel of a car parked in a fire lane near Finnegan's Grill with teammate Desmond Harris and Stonehill College football player Brandon Cox early Sunday when police officers approached the car.
The chief said about 150 people were milling around the bar.
It was "very chaotic," he said.
Henry allegedly drove off when one officer knocked on the driver's window. A second officer tried to stop the car, which accelerated, striking him and a third officer who tried to grab him from the car's hood, police said.
The officer clinging to the hood and another officer fired at Henry and the car came to a stop after striking a police cruiser.
"For unknown reasons, the operator sped away,'' Algano told the Globe.
Henry was dead at the scene, Cox was grazed by a bullet and four officers were treated for injuries, police said.
Algano said the shooting was being investigated by the New York State Police major crimes unit and the Westchester County district attorney's office.
Results of the investigation will be presented to a grand jury to decide if charges will be brought against the officers, Algano said.
Pace University President Stephen J. Friedman issued a statement extending condolences to Henry's family and friends.
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