I want to say I would keep it. But I'd probably give it back. I'm the kind of idiot that takes things back into the store if the checker forgets to ring it up.
I am the same way, I would give the money to the police, ask for a receipt, and then let the police decide how to handle it in order to return the money to the rightful owners.
But the thing is, I would think that legally whatever was left on/in the premises would become the property of the new owner, so if you decide to keep the money I don't think you would be legally wrong. Whether you are morally wrong by keeping the money is a question that only you can answer.
When we bought our house there were some things left here that we had to deal with. Most of the stuff we threw away, but there were a couple of items that we kept. But when it comes to money, people don't just leave money behind. Obviously the money was put there in an attempt to hide it. My guess is that the gentleman who died was an older person who probably lived thru the Depression and didn't trust banks very much.
Anyway, if you want to keep the money, then keep it. If you want to give it back, then give it back. It's entirely up to you.