Sure they can. One example is if they are charged with a felony.
I’m a little confused on this issue of arrests if Congress is not in session and also Schiff 4 Brains panic. First, it is my understanding that it is NOT illegal to lie on TV and second, regardless of what members say when they are on the “floor”, they are immune from a legal perspective. So my question is, what law can be used against Schiff 4 Brains? AND, on a side note, I recall Nobama signing an EO to allow “propaganda” in the news media. Can’t the media hide behind this EO (unless that EO is considered void - that Nobama was ineligible for the Presidency). Maybe Q’s drop about Nobama is leading to just that.