Car insurance premiums are not typically paid on a loan contract, but rather directly to the insurance company. You pay for future coverage and if you don't pay, then you have no future coverage, therefore no credit is being given to the consumer. In some situations, you may finance your premium through a premium finance contract but those contracts don't report to a credit bureau and again if you don't pay the collateral (coverage) is removed.
If you have outstanding balances or unpaid premiums for coverage received then a company will try to collect. If they can't collect they may forward to a collection agency. Those will negatively affect your credit rating.
Building good credit is important and paying your bills on time each month is an admirable way to start. Your credit history is something that the insurance company will look at when you start a policy and is part of many companies rating systems as well so it is important to build and maintain a good credit history.
Not having a credit history can make it hard to get insurance, purchase a car or get a house mortgage. A credit score is assigned by many insurance companies and it is based on your credit history including such things as bill paying history, the number and type of accounts you have, late payments, collection actions and outstanding debt. Your payment history typically makes up the most important aspect of this, about 35 percent usually.
Understanding How Your Credit History May Affect Your Car Insurance Coverage is an article in our learning center that you may find helpful.