(CBS News) — A death row inmate in California is getting high-profile support for a new round of DNA tests that could help exonerate him. Kevin Cooper was convicted for the 1983 murders of four people outside Los Angeles. He says he was framed. Sen. Kamala Harris said in a statement: “I hope the governor and the state will allow for such testing in the case of Kevin Cooper.”

CBS News’ Erin Moriarty has covered this case for nearly 20 years. She began investigating the story after receiving a letter from Cooper himself in 1999. He was convinced DNA tests would prove his innocence, but when the results came back, they were not what he had hoped for.

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It was called the Chino Hills massacre. On June 4, 1983, Doug and Peggy Ryen, both 41 years old, were found in their home hacked to death, along with their 10-year-old daughter Jessica and a young neighbor, 11-year-old Christopher Hughes.

Eight-year-old Josh Ryen’s throat was cut, but somehow he lived. Three weapons were used and Josh initially told investigators there were three attackers. But the multiple assailant theory was abandoned when investigators discovered Kevin Cooper next door. He’d been hiding out after escaping from prison on a burglary conviction.

In February, 1985, Cooper was convicted of the murders although serious questions remain. How did Cooper manage to use three weapons at once. The prosecutor’s explanation? He’s ambidextrous.

Cooper’s fingerprints were not found anywhere – just a single drop of blood that a state expert said was Cooper’s. The most troubling is the revelation that there was evidence pointing to another suspect and at testimony at trial, it was learned a sheriff’s deputy destroyed it.

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When Diana Roper, now deceased, found bloody overalls belonging to her boyfriend, a man with a violent criminal history, she turned them in. Floyd Tidwell was the sheriff at the time.

“Wouldn’t you say that taking in coveralls that appear to be covered in blood, not sending them to a lab and throwing them away before trial would be highly unusual?” Moriarty asked.

“I don’t know that that happened,” Tidwell said. “I’m very vague on that.”

In the early 2000s, the state conducted DNA tests on evidence from the case. The results matched Cooper. Cooper’s attorneys believe new and advanced DNA testing on existing evidence, including hair samples and blood, could support the theory that there were multiple people involved in the murders.

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There are many, including a federal appeals court judge, who believe the evidence that was previously tested back in 2002 could have been planted. The governor is reviewing Cooper’s request for additional DNA testing.