The agency had registered the case two days ago and today it got the case files from the state CID-CB, which had registered the case against the former Dairy, Khadi and Rural Industries Minister.
Sodala Police station had booked Nagar for allegedly raping a-35-year old woman, threatening and beating her on September 11 at his residence.
After registering the case, the police had referred the matter to the state's Crime Branch-CID as it involved a sitting MLA. The CB-CID had begun probing the charges.
CBI sources said Nagar would soon be questioned in connection with the case.