The FIR was registered by SP city unit president Mujeeb-ur-Rehman Babloo yesterday against one Deepa Bhatt, a resident of Jankipurm area here.
According to the complaint, Bhatt was approaching the administrative authorities for favours posing as a member of the SP's national executive.
The woman had also prepared her fake letter head, which claimed that she was a member of the national executive of SP and her official address was that of the SP office in New Delhi.
A case has been lodged under section 419 (cheating by impersonation) and 468 (forgery for cheating) of the Indian Penal Code.
Police said efforts are on to trace the woman.