Peterson is charged with murder in the death of Kathleen Savio, the third of his four wives. The hearing, which began more than two weeks ago, is expected to wrap up Wednesday, the Joliet Herald-News reported.
Savio was found drowned in a dry bathtub in March 2004. Prosecutors have argued Peterson killed his fourth wife -- Stacy Peterson, who is missing -- to prevent her from testifying in his murder trial.
Drew Peterson has not been charged in connection with the disappearance of Stacy Peterson.
An appeals court reversed a year-old trial court ruling that Drew Peterson's lawyers may be allowed access to prosecution documents, the Chicago Tribune reported. Defense attorneys sought to show Drew Peterson's prosecution on a gun charge was selective and vindictive.
The appeals court said there is no Illinois case law permitting pretrial discovery of prosecution documents in light of a defendant's claim of selective or vindictive prosecution.
Peterson was charged in November 2007 with possession of an illegal weapon. The gun was seized by state police on a search warrant dated Nov. 1, 2007, a few days after Stacy Peterson vanished.