Can I file a claim against landlord that is repsonse for parking at grocery?

As I was going to my car from the store I fell in the parking lot. When I got up I look and notice it was film protector from tablet. Both of my legs especially the right leg swollen and bruised immediately. Manager at the grocery store did a accident report and also there was a witness. She also made a report. Then later my family pick me up and went to the to ER and since then been seen by Orthopedic.