CBI sources said the agency has taken over probe from the Rajasthan Police which had registered the case against the former Dairy, Khadi and Rural Industries Minister following which he resigned.
The Sodala Police station had booked Nagar for allegedly raping, threatening and beating up the woman on September 11, after calling her to his official bungalow in Civil Lines in Jaipur on the pretext of giving her a job.
The woman has alleged that on some pretext the minister had taken her to his bedroom and raped her.
After registering the case under various sections of the IPC including 376 (rape), the police had referred the case to the state's Crime Branch-CID as it involved an sitting MLA. The CB-CID had begun probing the charges.
The woman's statement was recorded and her clothes, which she wore on the day of the alleged crime, were recovered and sent for forensic examination.
As per the normal procedure, CBI has started probe on the basis of FIR registered by the Rajasthan Police. CBI sources said Nagar would soon be questioned in connection with the case.
53-year-old Nagar has denied the charges, saying that his political rivals were trying to "frame" him ahead of Assembly elections in the state. He had resigned on September 20.