Testimony concluded Monday in an extended post-conviction hearing for Marlon Duane Kiser, who is on death row for the 2001 murder of Deputy Donald Bond in East Brainerd.
The Kiser defense team says new evidence points to Kiser's roommate at the time, Mike Chattin, as the real killer.
Chattin, who testified for the state at Kiser's trial in 2003, died in 2011.
Among the witnesses on Monday was Lisa Dooley Gray, who said she began living with Chattin in 2007 and stayed with him until he died - though she said he was a very violent man.
She said Chattin told her that a former girlfriend, Tina Hunt, had cheated on him, including with a police officer.
Ms. Gray said she once asked Chattin directly if he had killed Deputy Bond. She said he did not reply, but he made a face like he did when he was trying to intimidate someone.
The defense called a woman, who now lives in Nashville and was on the Kiser jury. She said she was given information about the new witnesses. She said if she had heard that testimony she would have voted for acquittal.
District Attorney Neal Pinkston said after the hearing he does not believe any evidence was brought forth that would necessitate a new trial.
Criminal Court Judge Don Poole, who will decide that issue, gave defense attorneys until June 5 to file a legal brief summing up their case for a new trial. The DA will then have three weeks to respond. Judge Poole will then give his decision.
The judge quizzed Kiser on earlier allegations he had against his initial attorneys.
Kiser said he is no longer raising that issue, but is going on the stance that the new evidence should give him a new trial and eventual acquittal.
He told the judge, "Either exonerate me or kill me."
It was the fourth different session in the post-conviction. Kiser has been brought back to Chattanooga each time from state prison.
At the end of the hearing he waved to family members and told them he loved them.