Well, who does have the authority to get you back to your home country when you flee? The only way I’m aware of to extradite people from one US member state to another is to get the Fed’s involved, since law enforcement from one state do not have authority in other states.
Federal courts can compel extradition, but I think they’d look at this matter as too political to consider.
But it makes no difference. None of the legislators have been accused of a crime* and there has been no extradition request.
* They are being accused of a violation of legislative procedure, not of a crime.