UPDATED 08/07/12 – 6:33 p.m.

JOLIET, Ill. (CBS) — The judge at Drew Peterson’s trial says he won’t let prosecutors use problems with the initial investigation into the death of the former police officer’s third wife to their advantage.

The question arose during testimony Tuesday as investigators took the stand to confirm they collected no physical evidence when Kathleen Savio’s body was found in a bathtub in 2004.

Defense lawyers complained prosecutors were trying to suggest that if investigators had done a better job they would have found evidence proving Peterson killed Savio.

LISTEN: WBBM Newsradio’s Mike Krauser Reports

Judge Edward Burmila, however, rejected a defense request to prohibit all testimony about the shoddy investigation.

But Burmila says he won’t allow prosecutors to imply that, had investigators actually looked for forensic evidence, it would have linked Peterson to Savio’s murder.

As CBS 2’s Mike Puccinelli and WBBM Newsradio’s Mike Krauser report, Will County Deputy Coroner Michael Vanover was first to the stand on Tuesday. The trial is now focused on the shoddy investigation following the discovery of his third wife’s body.

Vanover said he believed the circumstances of Savio’s death were suspicious, after she was found dead in a dry bathtub in her home.

“There were no signs of a fall or struggle in the bathroom, so I don’t see how she could have drowned. If a person had fallen, I am under the opinion the bottles would have gone flying. It was clean,” he said.

Vanover also testified he didn’t believe Savio would have ended up curled up in the tub if she had fallen.

“It’s a small tub, and the body was positioned in such a way that if a person would have fell, I don’t believe they would have came to rest that way,” he said.

However, Vanover testified that he didn’t follow the homicide-suspicious death protocol with Savio’s body because the state police investigator at the scene, Illinois State Police Trooper Robert Deel, didn’t believe it was necessary because he saw nothing suggesting it was a murder.

He did say that Deel placed paper bags over Savio’s hands.

Deel himself took the stand after Vanover, and testified he came up with an entirely different opinion of the position of Savio’s body. He concluded Savio died as a result of slipping in the bathtub.

“The position of the body was consistent with where it should be at the time of death,” he said.

LISTEN: WBBM Newsradio’s Mike Krauser Reports

Vanover also testified that he saw a towel on the tub when he arrived at the scene at 11:15 p.m. Previous witnesses who were in the bathroom have said the towel wasn’t there.

Prosecutors believe the towel was planted as part of Peterson’s work to stage the scene so it would appear that Savio’s death was accidental.

Defense attorneys were not impressed by Vanover’s testimony.

“Where’s the beef? I haven’t heard Drew tied to one miniscule piece of physical evidence, that he was any way, shape, or form involved in Kathy Savio’s death,” Joel Brodsky said.

Deel told jurors on cross-examination by Peterson’s attorneys that he didn’t see any evidence of injuries Savio would have suffered defending herself from an attacker.

“The general consensus among all of you was that there had been no sign of foul play anywhere in that house right?” defense attorney Joel Brodsky asked Deel.

“Correct,” Deel testified.

He also testified the coroner who did the original autopsy on Savio told him the death was not a homicide, and he never wavered in that opinion.

Pam Bosco, a spokeswoman for the family of Drew Peterson’s missing fourth wife Stacy, said, “From the very beginning, nobody was either listening, or they’re incompetent, or they didn’t care, or inexperienced. You name it.”

Bosco said she believes the original autopsy got it wrong, when Savio’s death was ruled an accidental drowning.

In Bosco’s view, Deel never really cared to investigate in the first place.

“You have also a state police officer who really didn’t really give a darn,” she said.

Prosecutors say Peterson staged the death, and did it well enough to fool investigators.

At a pre-trial hearing in 2010, Deel denied he had made up his mind about the case on the same night he examined the scene, while Collins testified it was at that time that Deel told him the death was accidental, the Chicago Tribune recalled.

Savio’s body was exhumed after Stacy Peterson, Drew Peterson’s fourth wife, vanished in October 2007. After a new autopsy, officials concluded that Savio’s death was a homicide.

Prosecutors and Illinois State Police believe Stacy Peterson is dead, and Drew Peterson has been named a person of interest in her disappearance. But he has not been charged in that case.

The trial resumed Tuesday after a three-and-a-half day break due to a sick juror.

A Bolingbrook police officer was also called to testify on Tuesday. He told about how he bumped into Drew Peterson at a divorce proceeding, saying Peterson ripped the attorneys for getting all of his money.

The officer claimed Peterson then said of Savio: “my life would be easier if she were just dead.”

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