I knew that answer would probably be controversial. The thing is, even moving the private key can be a problem because when there's no way of proving or finding who owns it. The person might come back to that spot, and try to find it. So, the very act of moving it or taking it could be morally wrong. However, then you have the issue of not moving it, and potentially allowing the next person to come along, and steal it. Giving it to the police, you assume they'll have some sort of moral decency, and influence, but probably not. I mean, they probably wouldn't know what to do with it, and you've already moved the private key at that point.

I'd probably trust myself more than the police due to the fact I know that I can trust myself to never take anything from the wallet, but I'm still not confident in moving it in the first place. I only said hand it to the police because of users who might read this, and I'm not sure I can trust many people to resist the urge. It's very easy for someone to go Ah, I've had this for a year now, and no one has claimed therefore it's mine, but I don't really agree with that either.

This is a massively complex problem, which doesn't have an easy answer that it might appear to have.