State Superior Court Judge Edward M. Coleman rejected the defense argument that evidence withheld by the prosecution made it impossible for Williams to get a fair trial.
The prosecution maintained that it unintentionally forgot to turn over notes and photographs from a weapons expert before the trial started, but that the defense suffered no harm.
Williams was not in court Thursday, following the birth of his second daughter on Tuesday.
Williams, 36, is charged in the February 2002 shooting death of a limousine driver at his mansion. The defense rested Wednesday after presenting five witnesses; the prosecution presented 36.
The defense has attempted to show that Williams was not aware that the driver, Costas "Gus" Christofi, 55, was in the bedroom with him while he was giving a tour to friends and members of the Harlem Globetrotters. Williams picked up a shotgun, snapped it shut and it fired, killing Christofi.
Williams faces eight charges, the most serious of which is aggravated manslaughter. He is also charged with attempting to make the shooting look like a suicide and persuading others to lie about it. Collectively, the charges carry up to 55 years in prison.
Williams retired from the New Jersey Nets in 2000 after a decade in the NBA, unable to overcome a broken leg suffered a year earlier in a collision with a teammate. He was suspended from his job as an NBA analyst for NBC after the shooting.