Hembree confessed to killing the three women during recorded police interviews, but later said the confessions were an attempt to cover up a string of armed robberies, according to the Gaston Gazette.
In the letter, Hembree also mocks the judicial system.
Hembree tells the citizens of Gaston County, N.C., that they should petition that state and force them to carry out his "murder sentence."
The Gaston County District Attorney's Office did not immediately respond to request for comment.
"I am a man who is ready to except [sic] his unjustful punishment and face God almighty with a clean conscience unlike you cowards and your cowardly system," Hembree wrote. "Kill me if you can suckers. Ha! Ha! Ha!"