If a car hits you in a crosswalk, you should seek medical attention and call the police. You should gather contact information for witnesses, and license, vehicle and insurance information for the driver. Of course, tending to your physical injuries comes first.
Law enforcement may issue a ticket or criminal charges against the driver. However, bringing your own claim for compensation is independent of any criminal charges. You have two years two file a claim, or six months if the claim involves a government body as a defendant.