K C Patel, the MP from Gujarat's Valsad, filed the complaint with the police last week following which the woman approached a city court, claiming police did not act on her rape complaint against the lawmaker.
The court has sought an action taken report in the matter and police have launched investigation. No rape case has been registered against Patel yet.
Police claimed it has emerged that the woman has been involved in similar instances earlier. However, her claim is being verified, police said.
Patel has alleged the woman invited him to a place in Ghaziabad for some work where she offered him a soft drink which was laced with sedatives, police said.
The MP claimed she threatened to file a rape case against him if he did not pay her Rs five crore.
Mukesh Kumar Meena, special commissioner of police, New Delhi range, said it was a "sensitive matter" and appropriate action will be taken.