A search of Grinstead's home produced very little evidence making the search for her very hard, the release said.
No other details about Duke were released in the press conference other than that he was a student at Irwin County High School, where Grinstead taught. Duke was never previously a suspect in Grinstead's disappearance, said GBI Special Agent in Charge J.T. Richardson.
After a 12-year investigation, the man police say killed Tara Grinstead, a 30-year-old teacher and beauty queen, is expected to make his first appearance in court on murder charges.
Grinstead vanished from her hometown of Ocilla in October 2005 and was never seen again.
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The GBI declined to say how they believe Grinstead died or if they have found her remains.
The case has stumped authorities for more than a decade. She was reported missing two days later when she didn't show up for work.
Investigators did talk with Grinstead's family members Wednesday, he said. "There was no struggle in the house", Grinstead's sister, Anita Gattis, told the Atlanta-Journal Constitution in 2006.
A massive manhunt was launched after Grinstead's disappearance, but the case proved hard due to the lack of evidence found in Grinstead's home, according to the GBI. If someone was removing her, she'd project her voice.