Auto Insurance Claims: Do I have to report my insurance about the accident if I have only liability coverage and the fault is at the other vehicle?

Question
QUESTION: My car was hit from behind while at a stop. It is at other driver’s fault. He has told the police the truth and apologized. My vehicle has no collision, comprehensive and medical but only liability coverage. So I have to claim with the other car insurance. The other car has no damage. The at fault driver will not claim with my insurance company. Under this condition, do I still need to report my insurance about the accident or just claim with the other car insurance directly? If I still need to report my insurance about the accident, can you explain why? I do not want my insurance know I had an auto accident because it is totally the other car driver's fault and I cannot claim anything with my insurance. Thank you for your answer.

ANSWER: You do not need to report this to your insurance company, if there is no coverage on your policy that might apply to this accident.

---------- FOLLOW-UP ----------

QUESTION: Thank you for your reply. I did not report my insurance about the accident but they still have known it. I have no clue how my insurance knows it. I have a follow up question. It was the other car fault but the other car has no damage. I do not think the other car driver will file any claim with my insurance. Can I ask my insurance to help me to file a claim with the other car insurance if my car has only liability coverage or I have to file a claim with the at fault car insurance directly?

Answer
If you do not have Collision coverage, your insurance company will not be making any payments, so they will not pursue the other driver's insurance company.  If you had Collision coverage, they could handle your damages and then subrogate against the other company.  Subrogation is the process where they collect their payments and your deductible from the other party.  

If you have an agent, he/she could provide you some advice though.