Yes, it is a civil matter Howard. But I can't get an attestation that it's a wildlife accident if I don't report it to the police. Without this certification, the insurance does not pay anything.
If it turns out that it was not game, but e.g. a pet, a pig or a cow, then the insurance does not pay via Partial coverage insurance.
If the animal had remained injured and motionless, or if it was killed, then I must remain at the accident place, until the police comes.