The thinking, experts say, is that Tesla can offer lower rates because AutoPilot will decrease the frequency of collision claims. The automaker would have a better determination of how safe drivers are based on how often they use AutoPilot and could adjust rates more easily than other insurers.

"They have a lot of confidence in their ?AutoPilot system," Jessica Caldwell, executive director of industry analysis at Edmunds, told Automotive News. "It seems as if they want to position that as their unique selling point. Offering insurance that takes it into account is fairly unique."

The automaker has partnered with Liberty Mutual since 2017 on a program called InsureMyTesla, although it's unclear whether the new insurance product would be connected. While details remain scarce, State National Insurance Co., a subsidiary of Markel Corp., has said it will manage the product.

According to a filing with the California Department of Insurance, State National said the Tesla-branded insurance would include, among other features, a customer-permitted direct data feed that would "eliminate frictional costs and inefficiencies inherent in traditional insurance processes." The filing also said that "vehicles equipped with an autonomous feature option will be eligible for credits based on the level of autonomy of the vehicle."

The automaker intends to eventually offer self-driving vehicles, although AutoPilot does not have that capability today.

Musk, on the April 24 earnings call, said if a driver uses the vehicle "in a crazy way," Tesla could raise that customer's insurance rates.

While auto insurance rates vary greatly and depend on factors including age, location and driving history, Teslas have generally been more expensive to insure than competing vehicles because of their technology and parts costs.

According to 2018 data from the Insurance Institute for Highway Safety, the Model S sedan topped a list of the 25 most expensive vehicles to insure.

Meanwhile, a 2019 study by Insure.com ranked the Tesla Model S as the 15th-most costly vehicle to insure in the nation, with an average annual premium of $3,300.

"Ownership cost is a big driver," Caldwell said. "They've had issues on delivering on price, and cheaper insurance could get buyers closer in line to what they were expecting to pay."