In his application to the SSP Lucknow, Thakur said he had given the complaint to Inspector of Hazratganj police station Vijay Pal Singh Yadav who initially refused to receive the complaint and has not registered the FIR till date.
He said Mulayam's statements were "definitely criminal intimidation", which is a cognizable offence and hence he has sought FIR.
Thakur alleged that Mulayam had threatened him over phone with dire consequences on July 10.
He said if the SSP did not register the FIR, he would move the CJM court.
The Uttar Pradesh government had suspended Thakur on July 13 and appointed the enquiry officer on July 14 to complete the enquiry within minimum time, asking him to assist in the enquiry in fullest measure.
Thakur challenged the order terming it as completely illegal.
In his petition before the Central Administrative Tribunal, he challenged the appointment of Chairman, Police Recruitment and Promotion Board VK Gupta as the enquiry officer against him and IG (Personnel) BP Jogdand as the representing officer.
Thakur said that as per Rule 8(6) of the All India Services Discipline and Appeal Rules an enquiry officer can be appointed only after getting a reply from the officer under Rule 8(5).
In his case, Thakur said, the charge sheet was issued on July 13 and received by him on July 15 but even before this, the state government appointed the enquiry officer on July 14, while he submitted his reply later on July 16.
Thakur dubbed this action as against the Rules and "politically motivated" after his complaint against Mulayam and sought quashing of appointment of the enquiry officer and directing the state government to decide further action only after considering his reply and his request under Rule 8(5) to be heard in person by the chief minister.
The IG-rank officer, was suspended within hours of approaching the Union home ministry in New Delhi on July 13 seeking a CBI probe into the rape case slapped against him.
The Samajwadi Party Mahila Sabha, meanwhile, demanded action on the rape charges levelled by a poor and Dalit woman, saying law should be same for all -- be it common man or police officer.
"Law is same for common man or police officer and we demand that action should be taken against him on the complaint of the woman," national president of Samajwadi Party Mahila Sabha Ranjana Bajpai said.
There should also be a thorough probe into whether Thakur and his wife have acquired massive properties by extorting money through RTI which they have been filing continuously even though the high court had asked them to do so only with the permission of senior authorities, she said.
Thakur is locked in a tussle with the state government over alleged threatening phone call by the SP supremo after which rape charges were levelled against him.
He was served a 200-page charge sheet and a vigilance inquiry was initiated against him.
Thakur stirred a political storm by releasing the text and audio of the conversation purportedly carrying Mulayam's voice.