It's the first time the death penalty has been applied in the Middle District of North Carolina for a carjacking resulting in death.
Atwater's attorneys make several claims in their request.
They say the death penalty is overreaching in this case because it has received a lot of media attention.
Second, the other defendant, Lawrence Lovette, Jr. has not been charged in federal court.
Finally, they say Lovette has not been charged in his alleged role in the murder of Abhijit Mahato, a Duke University graduate student who was robbed and killed in January 2008.
Carson was the UNC student body president at the time of her murder. Atwater and Lovette are accused of carjacking, kidnapping and killing her in March 2008.
Lovette will not face the death penalty because he was 17 at the time of the murder. He will be tried separately.