Hank Skinner is facing execution for the 1993 killings of his live-in girlfriend Twyla Busby and her two sons.
Skinner's lawyers say prosecutors violated their client's civil rights by not turning over crime scene evidence Skinner has maintained would exonerate him and possibly implicate Busby's late uncle as the real killer, the Amarillo Globe-News reported Tuesday.
At issue are seven items that were never tested: a blood-splattered windbreaker often worn by Busby's uncle, hair found next to her body, two knives, a rape kit, her fingernail clippings and a bloody dish towel.
Courts have rejected two previous requests by Skinner for DNA testing.
Initial DNA tests in 1994 showed Skinner had the victims' blood on his clothes, prosecutors said.
"(The courts held) Skinner could not show a reasonable probability that further testing would exonerate him," the state's brief in response to a motion brought by Skinner's lawyers says. "Skinner's third application for DNA testing will surely meet the same fate."