Yes all Insurance Companies do run your credit when they quote you a price for insurance whether for auto insurance, home insurance etc.
The credit check is used to see what your credit score is and your credit score is used to determine how risky you are to the insurance company.
When you have a higher credit score you'll see a lower insurance cost but when you have a lower credit score you'll usually pay more for your auto insurance or home insurance.
With a low credit score you may be denied home insurance but you can still get auto insurance although you may pay a higher price per month or year for your auto insurance.
Having a good credit score is necessary to get a lower insurance cost for auto insurance and homeowners insurance.