Nov 22 (Reuters) - General Motors' robotaxi unit Cruise is planning to re-launch in one unspecified city before expanding to others, just weeks after California barred its self-driving vehicles from public roads following an Oct. 2 accident.

The incident that took place in San Francisco involved another vehicle and ended with one of its self-driving taxis dragging a pedestrian.

"Once we have taken steps to improve our safety culture and rebuild trust, our strategy is to re-launch in one city and prove our performance there, before expanding," the company said.

The shift in strategy will result in reductions in personnel "primarily in non-engineering roles," Cruise said, adding that it would provide more details in mid-December.

The GM unit said it would focus on the Bolt-based Cruise AVs in the near term with a longer term strategy around the Origin, a multi-passenger vehicle designed without a steering wheel or other controls for operation by a human driver..

Cruise's woes have been a setback for an industry dependent on public trust and the cooperation of regulators.

As the company undergoes a safety review of its U.S. fleet, its CEO Kyle Vogt resigned on Sunday, a day after apologizing to staff. That was followed by the exit of co-founder and chief product officer Daniel Kan.

A GM spokesman said its finance chief Paul Jacobson would likely address the financial impact on the automaker during a call with analysts scheduled for Nov. 29.

Cruise unit had in recent months touted ambitious plans to expand to more cities, offering fully autonomous taxi rides.

As part of that, it had last year asked the National Highway Traffic Safety Administration (NHTSA) for permission to deploy up to 2,500 self-driving vehicles annually without human controls.

Without government approval, GM cannot deploy the Origin on public roads. The NHTSA said in July it "will issue a decision in the coming weeks" before the accident raised questions about the performance of Cruise vehicles.

Cruise also said it would compensate employees for potential tax liability of shares granted by the company. It had last week decided to make a new tender offer to allow employees to sell shares, two days after canceling an earlier offer.

Axios had first reported the news of the re-launch on Wednesday.

(Reporting by Samrhitha Arunasalam in Bengaluru, David Shepardson in Washington and Joe White in Detroit; Editing by Arun Koyyur)