Peterson is accused of murdering his third wife, whose body was found in a bathtub in 2004.
Prosecutors and defense attorneys clashed over Tuesday's testimony, forcing the judge to make a ruling.
The state is trying to prove that initial investigators that responded to Savio's home didn't do a good enough job processing the scene, and they want the jury to believe, if the crime scene investigators looked a little bit closer at the evidence there, they would have found evidence linking Peterson to Savio's death.
First on the witness stand was Michael Vanover, the Will County deputy coroner. He responded to Kathleen Savio's home the night she was found dead in her bathtub.
Vanover told the court, even though he believed Savio's death seemed suspicious, there was no evidence to support that, so he never told any investigators what he thought.
When the defense pressed Vanover on why he didn't come forward with what he believed, Vanover claimed he was following the lead of the Illinois State Police, which was heading up the case.
The state is trying to prove mistakes were made and homicide protocol was not followed. The defense tried to object to the prosecution's line of questions.
"The state wants to present evidence that somehow the investigation was, as they call it, 'botched,' and therefore they don't have evidence," said defense attorney Steve Greenberg. "Well, they may have evidence it was an accident, they may have evidence it was a homicide and someone else committed it, the one thing they don't have is evidence that Drew was in that house on that night."
When the state questioned Robert Deel, the crime scene investigator with the Illinois State Police, about why he didn't look for fingerprints or any DNA evidence outside the bathroom where Savio was found, or investigate a "spot cleaner" that was photographed. Deel said, "I was not thinking this was a homicide."
Deel testified there were no signs of a struggle or any foul play.
Pam Bosco, spokesperson for the family of Drew Peterson's fourth wife Stacy, who is missing, says the investigation seemed botched.
"What we're seeing right now, clearly from the start, Kathleen had everything stacked against her from the beginning," said Bosco. "Nobody was either listening, or they're incompetent, or inexperienced, you name it. From the start, Kathleen had everything stacked against her."
The last witness to take the stand Tuesday was Lieutenant James Coughlin of the Bolingbrook Police Department, another witness with hearsay testimony. Coughlin told the court Drew Peterson said during a divorce hearing about Savio, "My life would be easier if she were just dead."
In court late Tuesday afternoon, during a recess, the defense accused the state of sending a letter to the Illinois State Police complaining about how the investigation was carried out. When the judge asked them to produce the letter the defense could not do so.