Eric Clark was found guilty of first-degree murder and sentenced to life in prison. His lawyer argued that the then-17-year-old was "guilty except insane" and should instead be sent to a psychiatric facility.
"In his mind, he believed that the police officer was an alien," Clark's lawyer, David Goldberg, told justices.
All but four states — Idaho, Kansas, Montana and Utah — allow insanity defenses, but the ruling in Clark's case could force legislatures to change their laws.
Arizona allows defendants to claim they were insane at the time of a crime, but Goldberg said the standard to prove it is almost impossible, violating the constitutional rights of mentally ill defendants.
State lawyers said that their system guarantees that defendants are held responsible for crimes, if they are not insane, and argued that the Supreme Court should not use this case to declare for the first time a constitutional right to an insanity defense.
"The state has the right to define insanity as it sees fit," state attorney Randall Howe told the court.
Justice John Paul Stevens questioned if the state could execute someone who thought they "had a mission to kill aliens."
Other justices questioned what evidence was allowed in Clark's trial, and how it affected the outcome.
Clark was a promising football player and popular student until his behavior took a bizarre turn in the months before the millennium. He became convinced that aliens had taken over his town, Flagstaff, Ariz., as a "platinum city" and that his own parents were aliens.
Clark shot Flagstaff police officer Jeff Moritz on June 21, 2000, after the officer pulled over the teen as he drove around his neighborhood in a truck playing loud rap music. Moritz, 30, was the only police officer ever killed in the line of duty in the mountain community north of Phoenix.
Both sides agreed that Clark suffered from paranoid schizophrenia, but they disagreed on his legal insanity.
The Arizona law says a defendant "may be found guilty except insane if at the time of the commission of the criminal act the person was afflicted with a mental disease or defect of such severity that the person did not know the criminal act was wrong."
Lawmakers around the country imposed new restrictions on insanity claims following John Hinckley's acquittal by reason of insanity in the March 1981 shooting of President Reagan. Arizona changed its insanity law in 1993.
The Bush administration is backing Arizona, and its top Supreme Court lawyer, Paul Clement, told justices in a filing that "the insanity defense has always been highly controversial."
Sixteen states are also supporting Arizona and filed briefs warning justices that if they accept Clark's view of the case "it will call into serious question the validity of the majority of state insanity statutes."
Clark is supported by a variety of health groups including the American Psychiatric Association, American Psychological Association and American Association on Mental Retardation.
The case is Clark v. Arizona, 05-5966.