http://cdn.loc.gov/service/ll/usrep/usrep207/usrep207425/usrep207425.pdf
re:
https://constitution.congress.gov/browse/essay/artI_S6_C1_1_2/#essay-3
footnote 4
PANIC in DC
They are NOT immune from arrest in criminal cases.
It applies only to arrests in civil suits, which were still common in this country at the time the Constitution was adopted.
The phrase "treason, felony or breach of the peace" is interpreted to withdraw all criminal offenses from the operation of the privilege.
https://www.cbsnews.com/news/obama-administration-spent-36m-on-records-lawsuits-last-year/
Updated on: March 14, 2017 / 8:06 AM / AP
Obama admin spent $36M on lawsuits to keep info secret