No. of Recommendations: 1
Then THEY can be held because "something's wrong". They are held until the state says so.
They can't be held because "something's wrong."
ICE can detain you without a warrant if the detaining officer has probable cause to believe you are in violation of immigration law. Not because "something's wrong," but because they have sufficient basis for determining that there is probable cause that you're here illegally.
If a state officer has probable cause that an ICE agent has committed a crime, then they would be able to arrest them. But given the broad powers given to ICE agents as LEOs, I suspect that's going to be incredibly rare.
