The FIR was registered on a complaint filed by Joshi with the Crime Investigation Department under various sections of the Indian Penal Code relating to blackmailing and threatening, the state Director General of Police Swaraj Puri told PTI.
Investigation into the matter is continuing, he said, declining to give further details.
The case was registered under sections 387, 467, 471 and 507 of Indian Penal Code.
Joshi had resigned from the post of BJP general secretary resigned on December 27 after of surfacing of a Video CD that purportedly showed him in a compromising position.
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