[muawiyah]

Congress is "supreme" inasmuch as it can remove the other "branches". Within the Congress the House serves as the "prosecutor" in such cases and the Senate serves as the Judiciary (combined judge and jury sort of thing). In earlier times when Senators were chosen by state legislatures, it was quite clear to everyone that the sovereign states were in charge of the final court of judgment on the President/Commander In Chief and the Judiciary.

Still, notice that the Constitution provides that the House and Senate are judge of their own members.

In questions like this the Founders fell back on the elected body closest to the people to decide how to proceed in the case of a crime involving their members.

You might well read the Constitution someday to check all of that out.

[oceanview]

only with respect to official acts do they have such protections.

if a congressman murders someone inside washington DC, can they be prosecuted,or even investigated, for it by the civilian justice system?

[oceanview]

"...except treason, felony and breach of the peace, be privileged from arrest.."