Charles Harrelson is serving a life sentence in the death of U.S. District Judge John Wood, who was shot outside his San Antonio town house.
His lawyer argued in a court filing that Harrelson was not adequately represented at trial by his defense attorney. Harrelson claims that he was not in San Antonio that morning and that his lawyer failed to collect evidence that other people were responsible for the death.
Justices declined without comment to consider his case.
Prosecutors alleged that a drug kingpin paid $250,000 for the murder of the judge, nicknamed "Maximum John" for handing out tough sentences to drug dealers.
The case is Harrelson v. United States, 03-1241.
Harrelson, 65, is held at a maximum security prison in Florence, Fla., where his projected release date is 2051. Other residents of the same prison include Unabomber Ted Kaczynski and World Trade Center bomber Ramzi Yousef.