The trial opened Tuesday, with tearful testimony from neighbor Mary Pontarelli, who found Savio's body.
The death initially was ruled an accident but prosecutors brought charges against Peterson following the disappearance of his fourth wife, Stacy, and a re-examination of the evidence in Savio's death.
The defense sought a mistrial during Wednesday's morning session after Pontarelli's husband, Thomas, testified he found a .38-caliber bullet in his driveway after he had helped Savio change the locks on her house and Peterson told him, "Any friend of hers is an enemy of mine."
Prosecutors admitted they cannot prove Peterson, a former Bolingbrook, Ill., police sergeant, left the bullet for Pontarelli.
"The state's argument makes absolutely no sense to the court whatsoever," a visibly upset Will County Judge Edward Burmilla said in deciding to consider the motion, the Chicago Tribune reported.
"To say they want to put a witness on to say the defendant did something that intimidated him, but then say they couldn't prove it," meant jurors would be left with the impression that either Peterson threatened the witness -- despite the lack of evidence -- or that the witness, Thomas Pontarelli, was completely unbelievable."
Instead of a mistrial, Burmilla told the defense to decide whether Thomas Pontarelli's testimony should be stricken.