What about their responsibility to care for citizens' time, which is arguably more valuable than their possessions? What if someone had to go to the police station to get their computer and missed a job interview?
People are supposed to be free to receive and interpret any electromagnetic waves that cross their property, or in public spaces. Cops are people. So, they should be free to receive and interpret to any electromagnetic waves to further law enforcement, and in fact they would be foolish and incompetent not to. If your radio waves are saying "I'm a criminal" that's no different than posting a sign outside your house saying the same thing. If you don't want that, don't emit electromagnetic waves.