If you have no fault auto insurance will your insurance rates increase if you happen to be in an accident in which you were not at fault?

Generally speaking, no. However, in any moving incident/violation, your driving record is checked. If it turns out that you have a few past speeding tickets, and maybe another previous accident or two where you were not At Fault, the insurance company may choose to tag you as a high-risk driver and increase your premium. On the other hand, if you are a driver with a spotless record, your rates will probably not go up in the event of an accident where you are not at fault.