The suit by state Assemblyman Hakeem Jeffries and other parents claims that state Education Commissioner David Steiner shouldn't have granted a waiver to allow Hearst Magazines Chairwoman Cathie Black to take the job.
The waiver was needed because Black wasn't an academic.
The lawsuit says Steiner could only consider her own qualifications. Instead, the suit contends he granted a waiver as long as she hired a top academic adviser.
An earlier lawsuit challenges Black because she lacks an advanced degree.
The state Education Department declined to comment.
Steiner had praised Black's record of leadership and achievement.