When you look for auto insurance or other insurance and get quotes from either online or through an insurance office the insurance company will pull up your credit report to check your credit rating and credit score to determine your insurance rates on both auto insurance, home owners insurance, renters insurance etc.
However the Inquiry that the Insurance company pulls on your credit rating will not harm your credit like hard inquiries for loans, mortgages etc would.
So no looking for auto insurance or any other types of insurance will not harm your credit score.