Sources tell 9NEWS the federal public defender's office will argue that Dunlap was and is mentally ill, and that his trial lawyers didn't adequately present this information to the jury that sentenced him to death.
There were other issues with the trial as well. Including a claim, there was a conflict of interest between Dunlap's lawyer and a witness for the prosecution - among other issues.
The federal public defender's office has been appointed to represent Dunlap during the 10th Circuit Court of Appeals proceedings - a three-judge panel on Tuesday.
A state court sentenced Dunlap to death. The sentence then went through a series of appeals on the state level where the courts upheld the decision.
Eventually, the death penalty was challenged in federal district court. The federal court upheld the prior decisions of the state court, and that decision is what was being appealed Tuesday.
Paul Koehler with the Colorado Attorney General's office argued Dunlap should remain on death row. He cited Supreme Court cases where mental health status was not presented because it was deemed more damaging. Koehler says attorneys can reasonably decide not to present that evidence.
"[Dunlap's attorneys] were experienced defense attorneys with experience in 15 other death penalty cases," Koehler said.
He went on to say they made the choice not to present mental health testimony in court.
"The defense had very little to work with here," he said.
The three-judge panel heard oral arguments from both sides lasting 30 minutes each. No decision will be made Tuesday.
"In death-penalty cases, after the state is through with its proceedings the federal court looks at it as well," a source told 9NEWS. "This is a part of that review by federal courts of the death penalty imposed on Dunlap."
The judges will eventually issue their decision to both parties. There is no timeline when that could happen.
If Dunlap wins, his case goes back to state court, which will likely sentence him to life in prison. The state can appeal the decision.
If Dunlap loses after Tuesday's argument, his case could be appealed all the way to the U.S. Supreme Court. The court may choose not to accept the case.
"I was impressed by both the Attorney General's and the defense team," said James Peters, the former District Attorney in Arapahoe County. Peters was the Chief Deputy Prosecutor on Dunlap's case. "Mr. Dunlap has a thorough and effective counsel throughout the trial and appellate proceedings. For the sake of the victims, I hope this case will be concluded at a reasonable time. I think the judges were well prepared."
The future length of this case will depend on how long the judges will take to render an opinion, whether the Supreme Court will take the case, and if or when the state will set an execution date.
Sources tell 9NEWS it's not a question of weeks or years, it's a question of months.
Colorado does not have a long history of executing inmates, so it's hard to compare Dunlap's 16 years on death row to someone else.
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