The Utah Supreme Court will hear arguments in the case of a condemned inmate set to die by firing squad.
Ronnie Lee Gardner is scheduled to be executed June 18.
His attorneys filed an appeal seeking to stop the execution and asking for a review of Gardner's 1985 death sentence.
Gardner was convicted in the fatal courthouse shooting of attorney Michael Burdell.
The high court on Thursday set a June 3 hearing date and issued a schedule for attorneys to submit written arguments.
Gardner's attorneys will argue he was denied state funds to pay for experts and investigators who could have provided mitigating evidence during the penalty phase of his trial.