In a letter written to the state House and Senate leaders Tuesday, Atkinson asked legislative leaders to pass a law to restore authority to her job, give Perdue complete control over the Department of Public Instruction and let voters decide in a referendum.
The Legislature and State Board of Education have given and taken away power from the superintendent of public instruction since the 1990s.
The post currently has few duties although the superintendent is elected statewide by voters. Atkinson was re-elected in November.
"It seems logical that an elected official would be able to select, organize and run his or her state agency," Atkinson wrote in the letter. "You can rest assured that the over 2.1 million voters who voted for me think I have the authority to run the department."
Gov. Perdue has asked that the State Board of Education make her choice for board chairman -- former Cumberland County Schools superintendent Bill Harrison.
He would also serve as the CEO over the department.
Meanwhile, Perdue said Atkinson would continue to serve as an "ambassador" for the public schools.
The state superintendent position has often been a topic of discussion as some lawmakers and education advocates have recommended that role become an appointed position or be abolished.
The state constitution calls the superintendent the chief administrative officer of the board, whose voting members largely are appointed by the governor and are directed to supervise and administer the public schools. But legislation approved in 1995 gave the board flexibility to craft the superintendent's job.
Atkinson also asked legislative leaders to examine whether the education board is needed or whether the method for appointing its members should change.