Following the fatal crash on March 18, Uber took all its self-driving cars off the roads in the four cities they operate. Now, it's been revealed that the company won't be renewing its autonomous vehicle permit in California, which expires on March 31.

In a letter from the state's Department of Motor Vehicles to Uber, DMV deputy director and chief counsel Brian Soublet wrote: "Uber has indicated that it will not renew its current permit to test autonomous vehicles in California."

Uber's cars will no longer be able to operate on public roads in the state once the current permit expires next week. The company said it does not know when it will reapply for permission to test the vehicles.

"We proactively suspended our self-driving operations, including in California, immediately following the Tempe incident," an Uber spokesperson said, in a statement. "Given this, we decided not to reapply for California DMV permit with the understanding that our self-driving vehicles would not operate on public roads in the immediate future."

If Uber does apply for a new permit, it will need to "address any follow-up analysis or investigations from the recent crash in Arizona and may also require a meeting with the department."

Tempe, Arizona, police released a video of the accident last week, in which 49-year-old Elaine Herzberg was struck by an autonomous Uber Volvo as she pushed her bicycle across the road. She later died in hospital, becoming the first person to be killed by a self-driving car. The clip, which includes interior and exterior views, appears to have raised more questions than it answered.

The accident has elicited responses from other self-driving companies. Intel---the owner of Mobileye---said its software would have detected and classified Herzberg one second before impact.

Both Toyota and Nvidia have also decided to temporarily halt their autonomous driving tests on public roads, while Arizona has blocked Uber from testing the vehicles on roads within the state.

"The accident was tragic. It's a reminder of how difficult SDC technology is and that it needs to be approached with extreme caution and the best safety technologies," a Nvidia spokesperson said. "This tragedy is exactly why we've committed ourselves to perfecting this life-saving technology. Ultimately AVs will be far safer than human drivers, so this important work needs to continue. We are temporarily suspending the testing of our self-driving cars on public roads to learn from the Uber incident. Our global fleet of manually driven data collection vehicles continue to operate."