At issue was testing requested by death row inmate Melvin Bonnell, sentenced to die for killing Robert Bunner in Cleveland in 1987.
Attorneys for the 61-year-old Bonnell argue that if DNA testing of his clothes failed to detect the victim's blood it would rule him out as a suspect.
But the court noted in Wednesday's decision that Bonnell already unsuccessfully argued that point at trial because the state said then the victim's blood was not on the jacket.
The court also said other evidence against Bonnell was overwhelming, including eyewitness identification of him as the shooter.
Bonnell's attorneys called the decision disappointing.
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