Tesla, of course, is disputing the insurer's analysis.

"This analysis is severely flawed and is not reflective of reality," the electric-vehicle maker said in a statement emailed to Automotive News. "Among other things, it compares Model S and X to cars that are not remotely peers, including even a Volvo station wagon."

AAA' chief actuary said the insurer noticed the anomaly in its own data before confirming it with data provided by a second source, the Highway Loss Data Institute.

"Looking at a much broader set of countrywide data, we saw the same patterns observed in our own data, and that gave us the confidence to change rates," he said.

Other large insurance companies, including State Farm and Geico, said that claims data is a major factor in calculating premiums. But they would not disclose if their Tesla-owning customers would also see rates rise.