Brian David Mitchell was sentenced in federal court last month for kidnapping and sexually assaulting Smart. Prosecutors said Smart and her parents agreed to the dismissal, the Salt Lake Tribune reported.
State court officials said Mitchell's defense team has until July 12 to file a response to the dismissal motion.
Mitchell kidnapped Smart, then 14, at knife-point from her parents Salt Lake City home in June 2002. She was rescued March 12, 2003, when local residents spotted her on a Sandy, Utah, sidewalk with Mitchell and his wife, Wanda Eileen Barzee.
State charges against Mitchell sank into limbo when a judge declared him incompetent. He was convicted in federal court after a federal judge declared him competent to stand trial.