In Article I, Section 6, Clause 1, the Framers provided for Members of Congress to be free from arrest when attending or traveling to and from Congress except in cases of treason, felony, or breaches of the peace. In interpreting this provision, the Supreme Court has held that the phrase treason, felony, and breach of the peace encompasses all criminal offenses. Consequently, Members are only privileged from arrests arising from civil suits, which were common in America at the time the Constitution was ratified.
And here's the full Article 1, Section 6, Clause 1
Section 6: Rights and Disabilities of Members
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.
Ah. Referencing the actual Constitution. This is the way. Thank you, dec3169.
To save other anons the trouble, I'm copy/pasting your comment from that link below:
And here's the full Article 1, Section 6, Clause 1
You're welcome. I've always found this stuff interesting.