This is a little different spin on the average Craigslist scam. Instead of trying to get you to send them money, they lure you in with really cheap rent and try and get you to give up a lot of personal information.
You can read the whole story here, but I gave you the gist of it. The most interesting part of the story is the last sentence
Believe it or not, APD said it’s not a crime to claim you own someone else’s house and try to rent it out. However, it is identity theft if someone uses your personal information to steal from you.