No-Fault Doesn't Mean No Lawsuit
Having no-fault insurance can be advantageous in many cases as your medical bills are paid without having to argue over who was really at fault in a car accident. Another advantage is that negligence injury lawsuits aren't as common in these states as the no-fault law does not require determination of fault for insurance to pay out. However, that doesn't mean you can't be sued or can't sue someone who was technically at fault. The circumstances in which you can sue are limited, but they do exist. Should you find yourself ready to sue someone who caused an accident that left you injured, you'll need to speak to an attorney to verify that you have a case and can take the next legal step.
Costs That Exceed Coverage
Your insurance will cover your medical bills up to a certain limit. However, your actual bills may be larger than the coverage maximum, and you'd be expected to pay those costs out of pocket. In that case, if you are sure the other driver was really at fault and can prove it, you may be able to sue them to have the other costs covered by them or by their insurance. Note that since property damage isn't covered by no-fault policies, you could sue to get reimbursed for costs related to the repairs, too.
Pain and Suffering, Emotional Distress, and So On
No-fault insurance helps with medical costs, lost wages, and ordinary services, but it doesn't have a separate fund for pain and suffering. Yet if you were injured in an accident, especially one that was so severe that your bills exceeded your coverage limits, you're likely going to have emotional effects from the accident that keep appearing in your life over and over again. You can sue for such things, but you must be sure the person you're suing really was at fault. For example, if you're hit by someone who technically doesn't have insurance but who was driving someone else's car and covered under their insurance, then you'd sue the person who hit you and not the person whose insurance policy was used.
Severe, Life-Changing Effects From the Accident
Sometimes a state requires any non-monetary/non-property claim to show that the effects of the accident were so severe as to be life-changing. This can be kind of nebulous as even minor emotional issues stemming from the accident can stick around and give you nightmares for years. You'd need to speak with an attorney who has experience with these lawsuits to find out what your state requires and how much proof you'd need of the "life-changing" effects. For example, in one state, you might need a psychiatrist's report showing that you had crippling PTSD while in another, you might need only a therapist's letter noting that you've had recurring nightmares as a result of the accident.
Before you do anything else, speak with an attorney. You'll need the help of one anyway should you decide to sue.
For more information on no-fault claims, contact a professional near you.