Stacy Peterson, the defendant's fourth wife, disappeared in October 2007 shortly after asking Smith if she could get more in a divorce settlement by threatening to tell investigators her husband had killed Savio, the Chicago Tribune reported.
"She wanted to know if the fact that he killed Kathy [Savio] could be used against him," Smith testified. "She didn't use the word leverage, but certainly that was the intimation."
The investigation into Savio's 2004 death, which originally was ruled an accident, was reopened after Stacy Peterson vanished.
Peterson's son, Tom, had been expected to testify Wednesday but that testimony was put off after the prosecution admitted it had neglected to turn over a state police interview with him to the defense.
The defense opened its case Tuesday and was expected to wrap up this week, without the defendant testifying. The trial before Will County Judge Edward Burmila is in its fourth week.