The application said that as a social activist and mother of a young law student, Thakur felt that "it was her duty to register an FIR against such people who have committed these crimes as alleged by two young interns."
She said that the FIR must be registered in compliance with the recent Supreme Court order in Lalita Kumari versus State of Uttar Pradesh and others which has made registration of FIR compulsory.
Thakur claimed that she initially moved the application in Gomtinagar police station but no case was registered.
The case is likely to come up for hearing on Monday.
Two students of NUJS, a premier Law school in Kolkata, have levelled allegation of sexual harassment against two Supreme Court judges.
The apex court has formed a three-judge committee to probe the charges levelled by a law intern.
The allegation by the second girl surfaced on Friday. She had narrated her ordeal on a social networking site on November 11 under her own name but the comments have now been removed from it, reported the website Legally India, which first came out with the fresh allegation.