Well I'm no lawyer in the slightest, but in order to find us out they'd have to do something illegal which would then break the laws they set up because of all the security measures Bitcoin has, so the only way to catch anyone in their country using Bitcoin would be to get rid of the fifth amendment ( I think that's the one that prevents unreasonable search and seizures ) and in doing that they'd stop being any sort of legitimate government.
Or they could look at the companies that
openly say that they exchange Bitcoin for dollars?
That would seem like a pretty obvious start, wouldn't it?
And no, the fourth amendment protects against unreasonable search and seizure. The fifth protects against self-incrimination.
I don't even live in the US, and I know that.