The state Court of Appeals last year ordered a new trial because a judge denied Maye his constitutional right to be tried in south Mississippi's Jefferson Davis County.
Both Maye and prosecutors asked the Supreme Court to hear the case.
Maye was convicted and sentenced to death in 2004 in Marion County for the slaying of officer Ron Jones.
In 2006, the death penalty was dismissed and Maye was sentenced to life without parole.
Maye's trial was moved to Lamar County. Before trial, Maye petitioned the court to put the case back in Jefferson Davis County. A judge transferred the case to Marion County.