Mr. Gurley was killed on Nov. 20, 2014, by a ricocheting bullet fired by Mr. Liang, who was on a night patrol in a dark stairwell in the Louis H. Pink Houses in the East New York neighborhood.

Image Akai Gurley

Mr. Liang was convicted of involuntary manslaughter, and the Police Department fired him. But in April, Justice Danny K. Chun of State Supreme Court in Brooklyn reduced the charge to criminally negligent homicide, describing the shooting as essentially an accident. He sentenced Mr. Liang to five years of probation and 800 hours of community service.

The case frustrated many in the Asian-American community who felt that Mr. Liang, who is Chinese-American, was used as a scapegoat during a national debate about the policing of black communities. And many African-Americans protested the shooting, citing concerns with tactics used by officers in housing projects and drawing parallels to other fatal shootings of unarmed black men.

At the sentencing, Mr. Liang apologized to Mr. Gurley’s loved ones. “The shot was accidental,” he said. “My life has forever changed.”

The $4.1 million will be paid out in structured settlements to Akaila, starting when she turns 18 years old, though Ms. Ballinger may petition the court to receive a small portion, perhaps in the form of a monthly stipend, Mr. Rynecki said. A college fund will also be established for Akaila.