The drivers and others who are filing claims contact the insurance companies that are involved.
If the other driver was at fault, contact his or her insurer to make
your claim. Also, contact your own insurer if your policy requires it,
or if you are making any claims under your own coverages.
If you were at fault, contact your car insurance company to notify
them of the accident. Advise your insurer if others likely will be
calling to file claims or if you need to file one.
The police and DMV don’t call your car insurance company and tattle on you.