An FIR was filed against her over alleged loss to the exchequer when she was Inspector General of Prisons but the case was closed last year during the central rule in Delhi, the Congress said.
Congress leader Anand Sharma also targeted the Aam Aadmi Party over allegations that it had accepted funds from "dubious companies" in the run-up to the Lok Sabha polls last year.
Sharma said the Bharatiya Janata Party should answer why the FIR against Bedi was closed, and also about her being "removed" by some states where she was posted.
"When she was IG (Inspector General) prisons, there were some complaints. The Delhi High Court directed the Delhi Police to register an FIR. It was closed during central rule in Delhi," Sharma said.
He said the FIR concerned "misuse of position" which led to loss to the exchequer.
Congress: Bedi's FIR concerned "misuse of position"
Sharma said Bedi was brought as chief ministerial candidate for her administrative experience as there was "dearth" of leaders in the BJP.
"Why was she removed from Mizoram? Why she was removed from Chandigarh and Goa? If answers are not provided till tomorrow, we will disclose reasons," Sharma said.
"Are they fighting the polls with money from the common man or from fake companies? The whole truth should come out," Sharma said referring to allegations that the AAP accepted funds from "dubious companies" last year.