Grabbing a ride from Uber or Lyft? Now you can get an insurance policy from your phone for the ride too.

Startup SURE says it has partnered with underwriter Chubb to launch a new service that allows passengers to buy accidental medical, death and dismemberment insurance coverage for the ride.

While ride-hailing companies typically provide liability insurance coverage for U.S. drivers that would cover passengers in an accident, this product aims to fill in any potential gaps.

The program, called RideSafe, works by connecting a customer's Uber or Lyft account to their SURE Insurance app, and once coverage is initially authorized, the passenger's ride is automatically insured.

The company said Thursday that future versions of its RideSafe product will include coverage for passengers riding in autonomous vehicles used for ride-sharing.