Yes, there is still an option to buy personal accident insurance even after having it with your car insurance. PA insurance policy with car insurance is applicable during car accidents for owner-driver. The insurer will pay for the compensation in case of bodily injury due to road accidents. However, Individual PA policy covers you across given geographical territory under given risks such as falling from stairs, slips on the bathroom floor, road accidents, and more. Therefore, you can't rely on personal accident cove with car insurance and you should buy an individual personal accident insurance policy.