You can place a claim in the sense of contacting their insurance and asking them to pay, but the insurer will almost certainly defer to its customer, the apartment complex--remember: insurer's have a duty to their policy holders, not to third parties. So if the insurer should pay, it would be because it's concluded that you are likely to sue and relatively likely to win against it's insured, so it would be better to pay without the trouble and expense of litigation.Otherwise, you would to sue the apartment complex to seek reimbursement or compensation. You should be able to sue in small claims court, to reduce the cost of bringing a lawsuit. You would have to show both the apartment complex had some duty to protect tenant's cars, which may be very difficult to show (generally, apartment buildings and  businesses are not responsible for what happens in their parking) and also that it was in some fashion negligent--e.g. not reasonable lighting in the lot. The building is not responsible for it being a bad neighborhood.