One of the main factors in determining auto insurance is your driving record. This also may have an impact on your credit score, particularly if you have a propensity for getting in accidents.
First let us look at the vice versa case. Your score will unfortunately affect your insurance premium quote. Insurance companies believe that a person who has bad credit will generally be more likely to file an insurance claim on their car. This may be that a good credit score is indicative of long-term stability, and place more emphasis on how often you pay rather than how much you owe.
A person with a negative record may have citations; tickets and / or penalties related to speeding or parking convictions, aggressive driving, DUIs or other approv tacked onto their record. In general population terms, this bad record can be an indicator to credit companies that the driver is not particularly stable. If a driving record establishes that insurance has been evaded or not chosen for a period of time this may also indicate financial problems that will affect your credit score.
The ways in which your driving record can influence your credit score may not see particularly fair to you as an individual, particularly if you've had a run of bad luck with your car insurance claims even while maintaining a decent financial record elsewhere. Unfortunately, both insurance and credit work on generic risk assessments that pertain to an entire population in some cases. However, past history is far from the most important aspect of your credit score to credit companies, and any shortfall here should be outweighed by your good credit practices elsewhere.
If you notice your credit score being affected by claims made through car insurance or other parts of your driving record, it may be worthwhile contacting a credit company and explaining what happened on your driving record and ask them to improve your credit score.