Electric carmaker Tesla has hit a speed bump in China with questions being raised over safety and service just as local competitors gear up to challenge the US-based company in the huge Chinese market.

Tesla's road in China had seemed paved with gold after founder Elon Musk was granted rare permission to build a wholly-owned factory in Shanghai that has allowed it to accelerate to the head of the pack in China's electric vehicle (EV) market.

But a Tesla customer's protest at the Shanghai Auto Show on Monday has the company backpedalling after mounting pressure from consumers and officialdom.

A woman wearing a t-shirt with the brand's logo and the words "brake failure" climbed atop a Tesla model at the show, yelling that she was nearly killed when the brakes on her Tesla malfunctioned.

The scene quickly went viral on Chinese social media, where trigger-happy users often take aim at both foreign and domestic brands over perceived malfeasance.

Tesla appeared to have compounded the anger with an uncompromising initial statement that fanned the flames, prompting state news service Xinhua to say the company lacked "basic sincerity" and a host of Chinese official bodies to join the fray.

China's market watchdog agency on Wednesday night issued a short notice calling for an investigation of the woman's complaint, and the city of Zhengzhou where she is from has ordered Tesla to hand over data from her car to her.

The national market watchdog said it "attaches great importance" to the case, adding that it instructed local officials "to protect the legitimate rights and interests of consumers in accordance with the law".

Tesla followed up Wednesday with a more contrite statement on Chinese social media, saying it was in contact with Zhengzhou authorities and pledged to cooperate with an investigation and accept its conclusions.

Tesla is facing a backlash in China
Tesla is facing a backlash in China AFP / Patrick T. Fallon

Manufacturers cannot afford to trip up in China: with the government encouraging a broad shift to sustainable energy use, the country has rapidly become the world's biggest EV market and a vital industry prize.

Tesla was top of the heap in March, selling 35,478 of its cars in China, according to official government figures.

Second place with 29,413 sold went to the Wuling Hongguang Mini EV, made by a joint venture involving General Motors and state-owned SAIC Motor.

In a distant third was the Ora R1, a brand under Chinese carmaker Great Wall Motor.

Tesla is the highest-selling EV brand both globally and in China, where it sells one out of every four of its cars.

In China, it has stayed well ahead of a large pack of rivals both foreign and domestic but could face intensifying competition ahead.

Chinese tech giants including smartphone makers Huawei and Xiaomi, and even DJI, the world's top drone manufacturer, have recently announced big plans to enter the electric vehicle market.

The bad publicity in China caused Tesla's US-listed stock to fall five percent earlier in the week, but it has since gained all that back.