A question about physically controlling another player’s permanent

If my opponent takes control of one of my permanents (with cards such as Treachery or Mind control), am I obliged to give them my card and put it on their playmat? Or can I just put it near to them (but still in my playmat)? I’m asking this because yesterday someone was stealing cards from every opponent at the table, and two of them had the exact same sleeves, creating confusion over the ownership of the card afterwards. Or what if my opponent has dirty hands or something? Do I still have to give them my card? Is there an official rule about this?