Well, old 'happyroach' is showing his ignorance again!! Spouting verbiage with little or no knowledge of the facts!!
In answer to 'higgins':
Your post says that the car was parked in "your designated parking space". I assume that this is a multi-family location (apartment or duplex with assigned parking). If correct, the parking space is not yours and the owner can authorize the vehicle tow.
I must ask though.... since your post says that you do NOT have a lease, how is this your "designated parking space"??
Further, I assume that there are some posted or issued 'rules' that include specific requirements for any vehicles parked on premises. This could include 'must be in working condition", "must be currently registered and titled", "holding current and valid safety inspection", etc. and could authorize the towing of any vehicle that doesn't meet those requirements. If true, you have even less ground to stand on when filing your complaint.