Gary is to be executed for three of the seven rapes and stranglings of older women in Columbus in 1977 and 1978.
Carlton Gary, 67, is scheduled to be put to death Thursday evening at the state prison in Jackson in what would be Georgia's first execution this year.
Gary contented there was enough evidence to prove he was innocent of the crimes he is convicted off.
In August of 1986, Gary was convicted in Muscogee County of three counts of malice murder, three counts of rape and three counts of burglary and sentenced to death.
Prosecutors linked Gary to the string of nine similar murders in Columbus-plus others earlier in the NY cities of Albany and Syracuse.
The case was one of the most notorious in the state's history, terrifying a city as elderly women were raped and murdered in their homes and left with their own stockings tied around their necks.
He became a suspect when a gun stolen during a 1977 burglary in the upscale neighbourhood where all but one of the victims lived was traced to him.
Police arrested Gary six years after the last killing, in May 1984.
As a last resort, his attorneys filed four separate motions with Georgia Supreme Court, U.S. District Court Judge Clay Land of the Middle District of Georgia, the federal 11th Circuit Court of Appeals and the U.S. Supreme Court, seeking a stay on their client's execution, which was scheduled to take place 7 p.m. local time (8 p.m. EDT) Thursday.
The parole board met Wednesday to receive information for or against clemency and announced its members have been reviewing the parole case file on Gary for the past several weeks.
The lawyers claim that Gary is not the "Stocking Strangler" and that someone else is responsible for the multiple murders, the newspaper reported. This is especially significant, they contend, because the woman survived the attack and dramatically identified him at trial.
Bodily fluid testing done on semen found on Thurmond's body and on stains on Scheible's sheets also likely exclude Gary, his lawyers argue.
The state countered in court filings that the evidence Gary's lawyers cited had already been considered by the courts and that his convictions and sentence had repeatedly been upheld by state and federal courts over the past three decades. DNA analysis would have provided further evidence, they wrote, but it couldn't be done because the samples were discovered to have been contaminated at the Georgia Bureau of Investigation crime lab.
"Mr. Gary is not the Columbus Stocking Strangler", his lawyers wrote in their March 9 appeal to the U.S. Supreme Court.
Gary's lawyers have asked the U.S. Supreme Court to consider whether the Eighth and 14th amendments of the U.S. Constitution prohibit the execution of someone who is innocent if the evidence of innocence wasn't available at the time of trial.
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