Yes they can. They can attempt to put a restraining order on you as well.
Almost happened to me last month.
Detective calls me "Miss so and so said you were going to put a bomb in her car. You are facing terrorist threats and can be detained for up to 72 hours until this gets cleared up".
Me: "No I said "I was going to smog her car...not bomb...smog" she's crazy. She misunderstood me"
He believed me and left it alone. The lady had prior calls to 911 that didn't pan out, so he left it alone.