May 21, 5:41 PM EDT

Drew Peterson's lawyers appealing murder conviction

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Timeline of the Drew Peterson case

OTTAWA, Ill. (AP) -- Drew Peterson's murder conviction in his third wife's 2004 death should be overturned because of improper use of hearsay evidence and mistakes by his former attorney, lawyers for the former suburban Chicago police sergeant told a state appeals court Thursday.

The ex-Bolingbrook officer was sentenced in 2012 to 38 years in prison for killing Kathleen Savio. He remains a suspect in the 2007 disappearance of his fourth wife, Stacy Peterson, whose case prompted officials to re-open their inquiry into Savio's bathtub drowning.

Peterson's lawyers claim that Will County Circuit Judge Edward Burmila should not have allowed jurors to hear secondhand testimony from a pastor about conversations he had with Stacy Peterson, the Chicago Tribune ( http://trib.in/1ShZnNx ) reported.

A Third District Court of Appeals judicial panel did not immediately issue a ruling after Thursday's hearing.

Appellate attorneys are also challenging the trial judge's decision to allow Savio's divorce lawyer, Harry Smith, to testify about an alleged telephone call with Stacy Peterson in which she claimed her husband killed his ex-wife. The attorneys also argue that former defense attorney Joel Brodsky provided ineffective counsel and put his desire for publicity over his client's interests - claims that Brodsky denies.

Peterson, 61, also faces charges in an alleged murder-for-hire plot to kill Will County State's Attorney James Glasgow, who prosecuted the 2012 case. A trial is scheduled for early July in southern Illinois.

On Friday, a Randolph County trial judge will review a request by state prosecutors to allow cross-examination of Peterson, should he choose to testify. The court will also consider a request to discuss a 2003 attempt by Peterson to pay someone $25,000 to "take care of" Savio. A third motion to be considered seeks to limit discussion at trial about the details of a confidential informant's own criminal history.

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