They also said he showed them where Corporal Collins’s body had been found, but a transcript of a recording of the car ride does not indicate that he gave any directions.

Mr. Alley’s lawyers were unable to get information from him about the crime, so he was turned over to psychiatrists. One wrote that he “did not seem overtly delusional, except in his assessment of the police tactics and his belief that they would have beaten him if he had not confessed to the crime, said they could have gotten away with it because they were the police.”

The physical evidence in the case, analyzed with the primitive tools available in 1985, was suggestive but far from conclusive. On the driver’s door of the station wagon, authorities reported finding Type O blood, the same as the victim’s and Mr. Alley’s. Paper napkins from Danver’s, a regional restaurant chain, were on the floor of his car as well as near the body, the investigators said. Also in the car was proof that he had been in the vicinity of the crime: an air conditioner pump that had been installed earlier in the day at a house near where Corporal Collins had been running. Plainly, Mr. Alley had stolen it.

However, no traces of Corporal Collins — no fingerprints, hair or blood — were found inside his car or, for that matter, on Mr. Alley. No physical evidence showed he had been in a prolonged struggle with a 19-year-old Marine in excellent condition.

April Alley spoke to a reporter last month in Louisville, where she works in human resources for a hospital. As a teenager, she said, she was turned against her father by a hostile relative.

In her 20s, she reconnected with him at Riverbend Maximum Security prison. He was frank about his drug and alcohol use, she said, and told her that he had confessed under threat. She became inclined to believe him.