John Mark Karr was brought to Colorado from Thailand earlier this year, but he was released because his DNA did not match evidence found at the scene of the killing nearly 10 years ago, and because he had an alibi.
"He is not off the hook," Gary Phillips of the Department of Homeland Security told "48 Hours Mystery."
Investigators do not believe Karr killed JonBenet Ramsey, who was found strangled in the basement of her parents' home in Boulder, Colo. But they believe he might have criminal involvement with whoever did, the Rocky Mountain News said.
JonBenet Ramsey's father, John Ramsey, was also interviewed for the show, speaking publicly for the first time since his wife Patsy's death from cancer. John Ramsey said he feels some pity for Karr.
"After a while, he was so abused and vilified and convicted in the media that I started to feel sorry for the guy," Ramsey said.
Notable deaths of 2014 [PHOTOS]