Question:
Had a request to rent my apartment
Answers:
There are a number of scams like this going around, especially on eBay. They send you a cheque for too much money. You send them back the overpayment. Later, their cheque bounces. You have nothing and they have the "overpayment" you sent them back.
Just ignore them .. they probably have 100s on the go at the moment, so if you don't reply they'll move on to someone else. They only want someone's money!
HTH
Answers:
Total con, don't touch it.
Answers:
It's probably connected with International Fraud, don't touch it with a barge pole!