Unger's petition claims that a number of issues make a new trial necessary to protect his constitutional rights. He also asks that an attorney be appointed to represent him.
Unger exhausted his appeals years ago. His last recourse is a post-conviction hearing at which he could raise issues not raised on appeal.
Unger, now 48, has been serving a 30-year prison term in a Florida prison for burglary, grand theft auto, and assault.
Unger was convicted of killing off-duty Hagerstown police patrolman Donald Kline during a Dec. 13, 1975, armed robbery of Kim's Corner on Mulberry Street.
"This brings back a lot of bad memories for me," said George Siebert, a former Hagerstown Police captain who now is head of security for Hagerstown Housing Authority.
Siebert, a shift commander the night that Kline was killed, said he'll never forget that night. He later was involved in Unger's trial.
"Almost everyone involved in that trial is either retired or dead," Siebert said.
Those who have died include former Washington County State's Attorney John Hollyday, lead defense attorney Joseph Padula, and the Talbot County judge, Harry Clark.
Tried in front of a Talbot County jury in 1976, Unger was convicted of murder, armed robbery and other offenses and received a life plus 40-year sentence.
Sentenced to the Patuxent Correctional Institution, Unger escaped from that prison in 1981 by overpowering the driver of a dump truck and driving through an open gate.
He was captured and convicted of robbery later that year in Florida.
In 1990, Unger escaped from the Florida prison by using homemade wire cutters to cut away fencing over a period of time.
He was recaptured eight days later after he wrecked a car during a high-speed chase outside Strasburg, Va.
Returned to Maryland in January 1991, Unger was housed at the Maryland Correctional Adjustment Center in Baltimore.
Known as "Super Max'' and touted as escape proof, the Baltimore prison is where Maryland's 300 worst criminals are housed, prison officials said.
In December of 1991, a search of cells prompted by the escape of another inmate turned up saw blades hidden in Unger's cell, prison officials said.
Information on where Unger currently is incarcerated was not available Tuesday night.