I have heard of places doing that with your keys. They will make copies of it. The problem with that is it makes them suspects if that is the only place that your car has been left with the keys not in your posession. Sort of obivious if there is not forced entry. Unfortunately, the burden of proof is still on you

Doesn't that just suck?! You get your car broken into and you tell the cops, but your report will just be put into some file and you will become another case number that won't be dealt with. So, what do you do? You try to defend yourself when one night they possibly enter your home and you end up shooting one of them and then their family takes you to court and gets money from you...blah blah blah. Wonderful, isn't it?!