Bolingbrook police Lt. James Coughlin said he ran into Peterson, a sergeant in the department at the time, and his divorce lawyers in the Will County Courthouse in February 2004, a few months after Peterson's divorce from Kathleen Savio, the Chicago Tribune reported. Coughlin said another officer remarked the lawyers seemed happy and Peterson responded that they were getting all his money.
Coughlin testified Peterson then made a remark he remembered because Savio's body was found a few weeks later in her bathtub.
"My life would be easier if she was dead -- or died, I don't recall which word," Coughlin said.
Also Tuesday, a police officer who investigated Savio's death said he noticed a scrape on her left buttock but said there was nothing to suggest she had been killed. Robert Deel, who is with the state police, said he decided to wait for the autopsy to determine the cause of death.
Matt VanOver, a deputy coroner in Will County, said he noticed some suspicious circumstances. He said the bathtub was surprisingly clean and bottles of shampoo and other items were standing upright that would probably have tipped over if Savio had fallen.
"There was no obvious signs of struggle or foul play in the bathtub. I don't know how else she could have drowned," he said. "If a person would have fallen in that bathtub, I'm of the opinion that those bottles around the edge of that bathtub would have gone flying."
Savio was face down, which seemed like an unlikely position if she was the victim of an accidental fall, VanOver said. But VanOver acknowledged he did not tell investigators his misgivings at the time, and Savio's death was ruled accidental.
Peterson married Stacy Cales immediately after his divorce became final. When she vanished in 2007, the investigation into Savio's death was reopened.
Peterson has not been charged in his fourth wife's disappearance.
Celebrity Families of 2014 [PHOTOS]