"The woman's statement was recorded as per rules before the magistrate," IG Public Grievance A Mutha Jain here said.
The Ghaziabad-based woman had registered the FIR against Thakur under IPC sections 376 (rape), 504 (intentional insult) and 506 (criminal intimidation) on Saturday night.
Thakur's wife, social activist Natun Thakur, was also made co-accused in the FIR.
The woman in her FIR alleged that in November last year Nutan had come to Ghaziabad where during her meeting, she promised job to her and invited her to Lucknow.
Thakur had last week given an application against Mulayam alleging that he was threatened by the SP supremo and also released the audio of the purported conversation between them.