William Morva will not receive a new trial.
The Virginia Supreme Court dismissed the appeal from the convicted Montgomery County deputy and hospital security guard killer.
Morva's lawyer had filed a habeas corpus petition, claiming his convictions on capital murder while in custody were unlawful.
Investigators say Morva escaped custody in 2006 at what was then Montgomery Regional Hospital, attacked and killed hospital security guard Derrick McFarland, then shot and killed Montgomery County Sheriff's Office Corporal Eric Sutphin on the Huckleberry Trail.
During Morva's trial, his lawyer argued that the judge improperly refused to allow testimony from an expert witness.