Can I sue for the insurance for bad faith?

On 9/25/2019 my brother was in a car accident with my car, 09/30 I put a claim in with the other driver insurance since she was listed as at fault and cited for failure to yield. On 10/03 I received a voicemail from the claims adjuster saying the claim would be denied, she claimed there was a voice recording of my brother claiming he had the headlights off which caused her client to not see him coming, however this wasn't mentioned to the police, nor did she get a statement from my brother. That conversation ended with the adjuster saying she wasn't investigating anything and hanging up on me. Around 10/14 or 10/15 I called for a claim denial letter from the adjuster and was told she'll send it after her client goes to court for the citation, which was 11/07, the client was told that she has up until 01/31/20 to pay for my damages, now the insurance company is saying they'll only pay 60% liability. Based on this can I sue for bad faith and do I have to accept the 60%?