[sourcery]

US Constitution, Article I

Section. 6. The Senators and Representatives shall receive a Compensation for their Services, to be ascertained by Law, and paid out of the Treasury of the United States. They shall in all Cases, except Treason, Felony and Breach of the Peace, be privileged from Arrest during their Attendance at the Session of their respective Houses, and in going to and returning from the same; and for any Speech or Debate in either House, they shall not be questioned in any other Place.

There's nothing in there that prevents searches or other criminal investigations, nor anything that prevents criminal indictment. The language doesn't even make it clear whether Members have protection from arrest when not in the Capitol buildings or traveling to or from same.

[Freee-dame]

They shall in all Cases, except Treason, Felony and Breach of the Peace, be privileged from Arrest during their Attendance at the Session of their respective Houses,

Sounds like Felony to me.

[snowrip]

They shall in all Cases, except Treason, Felony and Breach of the Peace, be privileged from Arrest during their Attendance at the Session of their respective Houses, and in going to and returning from the same;

Which may be why Kennedy said he was on his way to a vote when he smashed up his car. Knew he was drunk, and attempted to get out of it.