1 In criminal matters, the hit-and-run party that caused the death should bear the full responsibility of the accident, and the other party should be detained now, waiting for being prosecuted and sentenced.
In civil affairs, as long as you get the accident responsibility letter, you should first apply to the police for mediation compensation. If the other party is willing, he can take the accident responsibility letter to the court to sue the other party for compensation.
Personal views are for reference only. You should ask your local lawyer or the judiciary for the details of the prosecution.