A death row inmate in Texas has sought DNA testing that he says will exonerate him, but he is scheduled to be executed on Wednesday.

The inmate, Hank Skinner, was convicted in 1995 of murdering his girlfriend and her two children, and has been seeking DNA tests of evidence from the crime scene since 2001. Texas, after years of controversy over its track record of executions, has strong laws on DNA testing of the previously convicted, The Texas Tribune reports. But Skinner's appeals have been "rebuffed," The Tribune reports, in court rulings that have found the new laws permitting re-testing of evidence do not apply to him or his case.

His appeal has to meet a strict standard: 

The 2001 law spelled out conditions under which inmates could get access to testing and established rules requiring law enforcement to preserve DNA evidence. Opponents, including some prosecutors and prison officials, worried that it would cause a flood of inmates to file requests. To address that concern, lawmakers adopted strict standards that required inmates to demonstrate not only that the results of DNA tests would prove their innocence but also would have prevented their being prosecuted.

But Skinner believes he has a case. And if his version is correct, his story is a heartbreaking case of caution on the part of defense attorneys that now could backfire against him terribly.

Some DNA evidence was presented at Mr. Skinner’s 1995 trial, and it showed that his blood was at the crime scene. But Mr. Skinner said that he had cut his hand on glass that had broken when someone else violently attacked his girlfriend and her sons. Mr. Skinner maintains that during the killings he was unconscious on the couch, intoxicated from a mixture of codeine and vodka (a toxicology report confirmed that he had high amounts of both in his system).

But because his lawyers feared the results might be incriminating, they did not seek testing on a rape kit, biological material from his girlfriend’s fingernails, sweat from a man’s jacket, a bloody towel or knives from the crime scene.

After the 2001 law passed, Mr. Skinner filed his first request for testing on the items, asserting that DNA evidence could prove that another man committed the crime.

Skinner's most recent request for testing was denied in a ruling published Thursday, the Associated Press reported. His attorneys plan to appeal to the Texas Court of Criminal Appeals.