The justices turned away an appeal by Adnan Syed, 39, who has been serving a life sentence since 2000 after being convicted in the strangling death of high school classmate Hae Min Lee.
Maryland's highest court in March ruled out a new trial for Syed despite his attorney's failure to properly defend him.
Prosecutors said Syed killed the 17-year-old Lee in 1999 in the parking lot of a Best Buy store shortly after school, and then buried her body in a shallow grave later that evening.