I received a letter from others insurance company told I am at fault

Received letter told me it was rear-ended the vehicle month ago and they found out me 100% at fault and would not pay out any damages caused to me. Do I need to take this up to my insurance or I will receive a bill from them because I didn't file a claim with my insurance? I went to the hospital at the incident and didn't exchange information and I was surprised they sent out a letter to my current residence and did the investigation. I haven't dealt with claim and auto insurance companies before so I don't know what the process is, please advise on how I should react to this.