Trooper Thomas Muehleisen said Williams led him to the body of Costas "Gus" Christofi, lying on his side on a carpet in a bedroom at Williams' Hunterdon County mansion.
Muehleisen said the victim had a sizable hole in his chest and a bloody white towel on his left side. The trooper said a shotgun was lying on the floor a few feet away.
Under questioning from defense attorney Michael T. Kelly, Muehleisen said he knew right away that Christofi could not have inflicted the wound himself with the long-barreled gun.
"It's obvious it wasn't a contact wound," Muehleisen said.
The trooper took the stand in the first day of testimony at the trial of Williams, 35, a retired New Jersey Nets center.
Prosecutors maintain that while Williams did not intend to kill Christofi, 55, he acted with reckless indifference when he took a 12-gauge shotgun from a cabinet in a bedroom and flipped it open and closed in one motion. The gun fired and hit Christofi, who was about 3 feet away.
The defense maintains that the shooting was an accident, and that Williams had not realized that Christofi had entered the room and was standing in front of him.
In opening statements Tuesday, prosecutor Steven Lember said Williams tried to cover up his role in Christofi's death.
"This defendant took the hand of a dying man and attempted to transfer the fingerprints of a dying man to the gun," Lember said.
Defense lawyer Billy Martin said the 2002 shooting was an accident.
"Jayson Williams will tell you how this horrific, totally unforeseeable, accident occurred," Martin said in his opening statement.
Lember insisted the shooting "wasn't any accident at all." He added: "That shotgun could not have fired without the defendant's finger on the trigger."
Martin, however, said the shotgun had no safety and a history of accidental discharge. He said evidence will show that debris in the shotgun may have contributed to its firing.
After Christofi was shot, "Mr. Williams panicked," Martin said. "He instantly dove on the ground, trying to comfort Mr. Christofi."
"Maybe he should have done some things differently, but he did not have criminal intent," Martin said.
Prosecutors said Williams wiped the gun and tried to put the victim's fingerprints on it, changed his own clothing, and told his guests to agree that the shooting was a suicide.
Martin said a Williams friend, Kent Culuko, who has pleaded guilty to evidence and witness tampering, suggested making it look like a suicide, and that he and others have adjusted their testimony after getting deals from prosecutors.
Williams faces eight charges, including aggravated manslaughter and witness tampering, that could carry up to 55 years in prison.