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.
Even in session they can be arrested for felonies (and likely any crime), though they don't want you to know that...
https://constitution.congress.gov/browse/essay/artI-S6-C1-2/ALDE_00013354/