(Adds lawmakers' letter to Uber and other automakers on legal issue)

By David Schwartz

PHOENIX, Ariz, March 22 (Reuters) - The daughter of the woman killed by an Uber self-driving vehicle in Arizona has retained a personal injury lawyer, underlying the potential high stakes of the first fatality caused by an autonomous vehicle.

The law firm of Bellah Perez in Glendale, Arizona, said in a statement on Thursday it was representing the daughter of Elaine Herzberg, who died on Sunday night after being hit by the Uber self-driving SUV in the Phoenix suburb of Tempe.

"As the first pedestrian death involving an Uber autonomous vehicle, the incident has sparked a national debate about the safety of self-driving cars, exposing the technology's blind spots and raising questions of liability," the law firm said.

The firm did not immediately return phone calls seeking more information.

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

The fatality 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. The specifics of how Uber's technology operates are not known.

On Thursday a group of 10 Democratic senators cited the fatality in Tempe in a letter sent to Uber and 59 other companies including Ford Motor Co and Tesla Inc highlighting how the use of forced arbitration clauses to settle customer disputes would prevent victims of accidents involving self-driving vehicles from exercising their legal rights.

The senators, led by Richard Blumenthal, a member of the Senate Commerce, Science and Transportation Committee, noted that Uber includes forced arbitration in its standard terms of service with users.

"Had the victim been a passenger ... the victim's family could have been denied recourse through the courts," the letter read. The senators asked the companies to commit to not using the arbitration clauses in contracts related to self-driving cars.

"When injury or death does occur, a forced arbitration clause would prevent consumers from exercising their fundamental legal rights as Americans," the senators wrote.

Many companies include forced arbitration clauses in contracts with customers, requiring that any disputes be settled in binding arbitration and barring customers from suing in a court of law. Arbitration rulings, generally, cannot be appealed.