You might want to suggest that if the insurance company doesn't provide you with the policy limits, that you will have no option but to contact a Personal Injury Attorney that will get the policy information through the lawsuit (Discovery) or sooner. Some state laws require disclosure. To be sure, check with a Personal Injury Attorney in San Diego (where you are from). It might not be a bad idea to get a free consultation anyway, just to make sure you aren't being short-changed by the insurance company - a practice that seems to happen more and more frequently. Good luck.
Be careful settling for "policy limits" unless you have it confirmed in writing. You should also obtain a declaration from the responsible party that includes, among other things, a statement that he wasn't working at the time of the incident (you could sue employer), and doesn't have an umbrella policy, etc.
If you had significant injuries, be very careful in accepting any offer. There are all sorts of tricks and non-disclosures, often leading you into accepting a low amount. An asset check should also be done if your injuries were severe and/or you will need future medical treatment.
Request in writing that the other party request in writing their insured disclose his or her limits. In California, we have a strict privacy act. You generally can only get policy limits disclosed in three ways from an at fault insurance company:
1. Written waiver
2. Your injury claim is worth the policy limits settlement or beyond
3. You file a lawsuit and request it in formal discovery
I hope this answers your question.
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