The evidence includes red underpants worn by the attacker and a saliva-stained bra worn by the victim, as well as socks, shoes and possible semen samples. It was collected near the body of the victim, Lance Cpl. Suzanne Collins, 19, who was found in a park next to the Millington Naval Air Station, where she had just completed an avionics program, in July 1985.

Modern DNA techniques were not available at the time, and when Mr. Alley asked for them to be used to test the evidence two decades later, courts in Tennessee refused. In 2011, five years after his execution, the state Supreme Court said it had been a mistake to deny the tests.

In April, Ms. Alley was named executor of her father’s estate as part of her attempt to seek the DNA tests. Mr. Alley, who had been an alcoholic and drug addict, had told her that he did not recall committing the crime. “He said, ‘If I did do it, I deserve what I get,’” Ms. Alley said. “‘But I don’t remember doing it.’”

Judge Skahan said state law governing DNA tests after conviction did not explicitly permit an estate to ask for them. No court in Tennessee had faced this issue before, she said, and the State Supreme Court might come to a different interpretation. The State Legislature could also act to permit the testing, she said.