By Joseph Hosey

JOLIET, Illinois (Reuters) - Opening statements are set for Tuesday in the trial of a former suburban Chicago policeman charged with murdering his third wife found dead in a bathtub in 2004, after suspicions were raised when his fourth wife disappeared three years later.

Drew Peterson, a former cop in the Chicago suburb of Bolingbrook, is charged with killing third wife Kathleen Savio, who was found by Peterson and some neighbors dead in her dry bathtub in March 2004.

State police investigators decided almost immediately that Savio perished in a freak bathtub accident and did not scour her home for murder evidence.

They reviewed that conclusion after Peterson's fourth wife, Stacy Peterson, disappeared in October, 2007. She has never been found and police presume she is dead.

Following the disappearance of Stacy Peterson, authorities exhumed third wife Savio's body and a new autopsy suggested she had been murdered.

Peterson was charged with murdering Savio but has not been charged in the disappearance of Stacy Peterson despite being the only suspect in what police describe as a "potential homicide."

The strange circumstances involving Peterson's last two wives have drawn national attention to the case. Even before the trial began, the Lifetime television network aired in January a movie called "Untouchable," starring Rob Lowe as Drew Peterson.

The movie garnered record ratings of nearly 6 million viewers for the network.

Experts said the case could be tricky to prove for prosecutors because of the lack of physical evidence. Prosecutors are expected to try to use statements made by Stacy Peterson, who they say told others before she disappeared that Peterson killed third wife Savio.

The judge presiding in the case, Edward Burmila, already has dealt prosecutors a blow, saying the jury cannot be told Stacy Peterson is missing and possibly dead. Jurors will only be told that she is not available to testify.

(Editing by Greg McCune and Philip Barbara)