Koschman died nearly eight years ago after being hit by Richard Vanecko, a nephew of former Chicago Mayor Richard Daley. Vanecko was never charged.
The Koschman family believes political clout played a part in the decision not to file charges.
The court hearing brought back painful memories for Nanci Koschman, David's mother. Her son died more than a week after Vanecko punched him in the head after leaving the bars at Dearborn and Division.
"I just want to see justice for David," she said. "It was hard to hear."
"It is a case in which the target of the investigation was a member of the most powerful political family in the state of Illinois," said Locke Bowman, Koschman's attorney.
In Cook County Circuit Court Thursday, the Koschman family's attorneys asked a judge for a special prosecutor to be assigned to the case. They allege that the investigation into the 21-year-old's may have been influenced by Vanecko's relationship to Daley. At one point in court, they held up a note uncovered from the files reading "The Daley sister son."
"I just want to see justice for David," Nanci Koschman. "I just really want the truth to come out. He was the most important person in the world to me. And I just want to know that it's going to be handled fairly."
Cook County State's Attorney Anita Alvarez has said that a special prosecutor isn't needed.
In court, a prosecutor said the law has been followed and there have been no improprieties. They also said that the case is now being investigated by police for a third time. There was also a second reopened police investigation in 2011. Police reports say it showed that Koschman, 5 feet 8 inches 140 pounds, was clearly the aggressor and Vanecko, 6 feet 230 pounds, was taking action to defend himself.
"We have a record in this case in which six witnesses say that Koschman was not aggressive, that this was a verbal confrontation that suddenly and inexplicably escalated with a single blow that resulted in Koschman's death," said Bowman.
Cook County state's attorneys declined to comment. Attorneys for Vanecko were also in court. They, too, declined to comment.
A judge will make his decision on whether to appoint a special prosecutor next Friday.