By Joseph Hosey

JOLIET, Illinois (Reuters) - A judge rejected a second request to declare a mistrial in the case of former suburban Chicago policeman Drew Peterson accused of killing his third wife, who was found dead in a dry bathtub in 2004.

There is little physical evidence linking Peterson to the death of Kathleen Savio, so prosecutors have been trying to introduce testimony this week that Peterson made threats and tried to hire a hit man.

Defense attorneys have objected to the testimony as hearsay, and have asked twice for a mistrial.

Will County Judge Edward Burmila again on Thursday rejected the request, and testimony resumed.

Peterson was not initially charged with murdering Savio, as her death was ruled an accident. But when Peterson's fourth wife, Stacy Peterson, disappeared in 2007, suspicions were raised and the Savio death was ruled a homicide. Stacy Peterson has never been found and is presumed dead.

The Peterson case has drawn national attention and was the subject of a Lifetime television network movie "Untouchable" starring Rob Lowe as Drew Peterson. His first and second wives have remarried.

(Writing by Greg McCune; Editing by Leslie Gevirtz)