The United States Supreme Court has held that the speech or debate clause applies to congressional aides, insofar as the aides conduct would be a protected legislative act if performed by the Member himself; but it does not extend immunity to the Member's aide when testifying before a grand jury about acts done by the Member or himself, if such inquiry does not impinge upon the legislative process, and proves relevant to investigating possible third party crimes.
Gravel v. United States, 408 U.S. 606 (1972).
Louis L. Brunetti,
Constitutional Law - The Speech or Debate Clause and Immunity for Congressional Aides,
Duq. L. Rev.
Available at: https://dsc.duq.edu/dlr/vol11/iss4/10