With gas up about $1 from a year ago, a new study found that cutting back on driving can lead to savings in auto insurance.

The study, released by the Consumer Federation of America, said that drivers who get behind the wheel less often than they used to can save an average of 5 to 15 percent on their auto insurance rates.

"Auto insurance rates are partially based on how much you drive and how you use your car," said J. Robert Hunter, director of insurance for CFA. "If you drive less to save money on gas, these driving changes might mean that you qualify for immediate insurance rate relief."

The CFA said that if you no longer drive to work or school, your insurance classification will change to "pleasure," which could get a 10 to 15 percent savings. Driving to a train or bus station and not all the way to school or work can also mean having your insurance classification change, leading to a 5 to 10 percent savings in insurance.

"While these savings will vary based upon the specific auto coverage you have, it is certainly worth a call," said Hunter. "Simply explain the actions you are taking to drive less and estimate how many fewer miles you are driving a month. Tell the agent or company representative that you want the cheapest rate they have for drivers reflecting your new driving circumstances."

Earlier this week, the CFA called on the nation's governors to require insurance companies to lower rates as Americans drive less.

"As Americans drive less because of the price of gas, fewer claims will be filed with insurance companies," said Hunter. "Whether this will mean windfall profits for insurers or rate cuts for the consumers is up to governors and state regulators to determine."