Lt. Saul Rodriguez, the public information officer of the Santa Monica Police Department, said he knew of three or four serious scooter injuries that he believed would require long-term treatment.

“That’s if they ever recover,” he said. “Knock on wood, nobody has died.”

The imminent return of the electric scooters to San Francisco, even in smaller numbers and in a limited one-year pilot, puts pressure on the doctors and public health professionals working on a taxonomy of e-vehicle types, sorting out shared and not shared, with or without a helmet, severity of the injury, and so on.

“The ideal is to be ready with standardized data-collection instruments when the pilot rolls out,” said Megan Wier, an epidemiologist with the San Francisco Department of Public Health.

With the clock ticking, Ms. Wier and her colleagues combed through months of police and hospital records to help inform the classifications. But she believes the most useful injury patterns will emerge only after a data schema is established and the scooters return to San Francisco.

In California’s Legislature, there is a movement afoot to loosen some regulations on the scooters. Assembly Bill 2989 would relax helmet requirements, stipulate that only riders under 18 need to wear protective headgear and allow electric scooters to be used freely on streets with speed limits up to 35 miles per hour, rather than the current limit of 25 m.p.h.

Bird, which has pushed hard for the bill, pointed out that adults riding electric bicycles are not required to wear a helmet. The company said it had passed out some 40,000 free helmets to its riders, but nonetheless felt the bill’s passage would provide riders with “more consistent ridership rules.”

Euwyn Poon, president of Spin, another scooter company, said it was “sensible” to allow electric scooter users to ride without a helmet, even on streets with higher speed limits.