Normally, your insurance rates will not increase if you are not responsible for a car accident. That’s because the at-fault driver’s insurance company is responsible for any medical expenses and vehicle damages. If your insurance company does not give any money out of their pocket, your rate will not go up.
The information in this answer is general in nature and is not legal or insurance advice for your specific situation. Policy language varies carrier by carrier; your declarations page is the final word. If you're unsure, call your agent before you need to file.