The court has sought the state government's reply on her application.
Sources said the FIR against Chinmayanand does not include rape charges and the law student wants him to be charged with rape.
According to legal experts, a miscellaneous application is a "formal expression of request submitted by way of an application, filed before the criminal court in or otherwise in the criminal proceedings on different actions of reliefs for some privilege, right, benefit or for an action".
Meanwhile, the Special Investigating Team (SIT) on Tuesday submitted its progress report in the case to the court in a sealed envelope.
The SIT informed the court that the forensic report on the video clips would take about four more weeks.
A division bench of the Allahabad High Court is monitoring the progress in the case, on the directives of the Supreme Court.
The woman, who was a law student at Shahjahanpur's SS College run by Chinmayanand, had on August 23 posted a video on the social media accusing the former union minister of sexual harassment and blackmail.
The woman went missing the next day and was found in Dausa in Rajasthan after the Supreme Court took cognisance of the matter.
Speaking to the judges in their chamber, she narrated her ordeal of the sexual harassment and blackmail at the hands of Chinmayanand.
She later filed a FIR in Delhi, while Chinmayanand filed a FIR alleging extortion threat from the women and three men.
Video clips of Chinmayanand taking a massage from the alleged victim surfaced on the social media and another video clip of the woman and her male companions discussing the extortion matter also surfaced on the social media.
Chinmayanand was arrested on September 20 and five days later, the law student and her male companions were also arrested. All are now lodged in the Shahjahanpur jail.
( With inputs from IANS )