The missing woman's relatives say the test could prove Drew Peterson's theories surrounding his wife Stacy's disappearance. She was last seen October 28.
Drew Peterson, 53, has denied wrongdoing, saying he believes 23-year-old Stacy left him for another man and is alive. Peterson has since resigned from the Bolingbrook police force.
Volunteers helping look for Stacy Peterson have apparently been told by police to look out for a 'blue barrel' that could been used to dispose of Stacy's body.
"If you stand by what you say, take a lie detector test," said Joel Brodsky, Drew Peterson's attorney.
"It really shows the lack of credibility of these statements that are coming out," said Pamela Bosco, Stacy Peterson's family spokesperson.
According to an Associated Press report, officers responded to Drew Peterson's house 18 times on domestic disturbance calls when he was married to his third wife, Kathleen Savio. But police never arrested him.
Department inquiry apparently found no indication that officers did anything wrong or violated procedure.
Kathleen Savio died in 2004. Police have said her death may have been a homicide staged to look like an accidental bathtub drowning. They are re-examining the case.