The court announced late Monday it would not stay Friday's scheduled execution of 50-year-old Cal Brown for the 1991 rape and murder of Holly Washa.
Gov. Chris Gregoire told The Seattle Times she was being briefed on the case and would not comment on whether or not she supported the death sentence being out.
Brown's lawyers have vowed to continue their appeals.
Brown was convicted of kidnapping Washa in a car-jacking near the Seattle-Tacoma International Airport and then taking her to a motel where he sexually assaulted, tortured and eventually killed her.
Members of Congress to keep receiving porn magazine
Justin Bieber crashes Drake Bell's album release party