Mr. Brown, 40, of Canton, Ohio, was killed on May 7 when the Tesla he was operating collided with a tractor-trailer in Williston, Fla. Tesla has confirmed that the Autopilot feature, which the company described as being in a “public beta” test, was activated before the crash.

Florida authorities and the National Highway Traffic Safety Administration are investigating.

There are proportionally few cars with self-driving features currently on the road, so the issue is a new one. Fewer than a dozen states, including Florida, have enacted regulations specifically addressing self-driving cars, according to the National Conference of State Legislatures.

Many truly self-driving cars are part of fleets being tested by auto manufacturers or companies like Google, rather than cars sold to private buyers. Such companies typically self-insure or carry special fleet insurance that applies if the cars are involved in an accident, said Hilary Rowen, a lawyer with Sedgwick in San Francisco who represents insurers.

Features like Tesla’s Autopilot, Ms. Rowen said, should really be considered driver-assisted systems, rather than true self-driving technology, which allows the driver to be a mere passenger. Tesla’s system is a sophisticated combination of various driver-assist features, she said, but Tesla warns drivers to “keep their hands on the wheel and eyes on the road.”

Mr. Hartwig said it was too soon to say how self-driving systems would affect insurance rates. “The technology is so new that there’s not a lot of actuarial data” to determine whether it significantly affects the frequency or severity of accidents, he said. Insurers, as they have done with other advances, from seatbelts to newer features like airbags and rollover prevention systems, gather information over time and adjust rates to reflect the impact of the changes, if warranted, he said.

But the very nature of self-driving technology may make it challenging to apply data from the cars to insurance premiums, Ms. Rowen said. “This is going to be a disruptive technology for the insurance industry,” she said. That is because computer software running the systems is continuously updated. So while insurers generally track trends with a certain make and model of car, the safety performance of an individual self-driving car may actually change over time, as software updates correct problems.

These issues will probably take as much as a decade to sort out, she said. In the future, during the claims process insurers may seek data from more sophisticated versions of black-box recorders to shed light on the cause of an accident. “Is it a driver problem?” she asked. “A software problem? Or some sort of muddle of the two?”

The Insurance Information Institute, in a report last year on self-driving cars, said the industry must study whether accidents with autonomous cars lead to more product liability claims, in which drivers blame carmakers or suppliers for accidents, rather than their own driving behavior. “Liability laws might evolve,” the institute noted, “to ensure autonomous vehicle technology advances are not brought to a halt.”