Is it obligatory to search for the person who vandalized the car and file a legal complaint against them, or is it sufficient to entrust the matter to Allah?

You are not obligated to inspect the camera device to identify the culprit, nor are you required to sue him; rather, it is permissible for you to do so. It is also permissible for you to pardon him, for the oppressed has three options concerning his oppressor, all of which are permissible, and some are better than others. If you wish to sue him, then you must inspect the camera device and file a complaint.