Merlin Hill had sought approval for a post-conviction appeal of his conviction and sentence. The 5th U.S. Circuit Court of Appeals denied Hill’s petition in January. The Supreme Court upheld that ruling without comment Monday.
Hill also argued the courts had ignored the results of a psychiatric evaluation.
Capital rape involves sexual relations with a child under the age of 14.
Court records show Hill had moved to the Tishomingo County area from Michigan to work on the NASA space project. Prosecutors said the sexual attacks occurred over a 3- to 4-year period.