By David Schwartz

PHOENIX, March 30 (Reuters) - More family members of a woman killed by an Uber Technologies Inc self-driving vehicle have hired legal counsel, indicating the ride services firm's legal problems may not be over in the first fatality caused by an autonomous car.

Phoenix attorney Patrick McGroder said he has been retained by the mother, father and son of Elaine Herzberg, 49, who died after being struck by an Uber self-driving SUV while walking across a street in the suburb of Tempe earlier this month.

On Thursday, a different law firm representing Herzberg's daughter and husband said it had reached a settlement with Uber. The terms were not given.

That settlement does not affect the new case, McGroder said in an email on Friday.

"We are in the initial stages of investigation," he said, noting he and his two partners will represent the family members and that they had sent a letter of representation to Uber this week.

A spokesman for Uber declined to comment.

The fallout from the accident could stall the development and testing of self-driving vehicles, designed to eventually perform far better than human drivers and to sharply reduce the number of motor vehicle fatalities that occur each year.

Uber has suspended its testing in the wake of the incident. Toyota Motor Corp and chipmaker Nvidia Corp have also suspended self-driving testing on public roads, as they and others await the results of investigations into the Tempe accident, believed to be the first death of a pedestrian struck by a self-driving vehicle.

The March 18 fatality near downtown Tempe also presents an unprecedented liability challenge because self-driving vehicles, which are still in the development stage, involve a complex system of hardware and software often made by outside suppliers.

Herzberg was pushing a bicycle while walking across a four-lane road outside a crosswalk when she was struck. Video footage from a dash-mounted camera inside the vehicle, released by Tempe police, showed the SUV traveling along a dark street when the headlights suddenly illuminated Herzberg in front of the SUV.

Other footage showed that in the seconds before the accident, the human safety driver behind the wheel was mostly looking down, not at the road. (Reporting by David Schwartz in Phoenix Writing by Chris Prentice Editing by Susan Thomas)