Jury selection began on Tuesday in a California courtroom over whether Elon Musk committed fraud with a pair of 2018 tweets saying he was poised to take Tesla private.

The tweets sent the Tesla share price on a rollercoaster ride and Musk is being sued by shareholders who say the tycoon acted recklessly and cost them billions of dollars.

The trial is expected to last three weeks and comes at a sensitive time for Musk, who will likely be called to testify.

Tesla's share price has plummeted over the past year with investors upset over Musk's buyout of Twitter, the social media platform where the billionaire appears to be devoting much of his attention.

Shareholders filed suit against Musk in 2018 for allegedly costing them billions of dollars with a tweet that said "funding secured" for a project to buy out the publicly-traded electric automaker.

In a second tweet, Musk added that "investor support is confirmed," and that the deal was only awaiting a vote by shareholders.

"The plaintiff alleges that these tweets were materially false and artificially affected the price of Tesla stock and other securities after they were made," US District Court Judge Edward Chen said while summarizing the case for potential jurors.

Musk's short tweets in 2018 have already been scrutinized by US authorities.

The country's stock market regulator, the Securities and Exchange Commission, ordered that Musk step down as chairman of Tesla's board and that the company and Musk each pay a fine of $20 million.

Musk denies he was being deceitful and his lawyers are expected to call on witnesses to vouch for his plans at the time, including testimony from Musk's friend and fellow billionaire Larry Ellison.

Picking jurors began after Chen last week refused a request by Musk to transfer the proceedings to Texas, the southern state where Musk has moved Tesla's headquarters.

- Twitter ban request -

Lawyers representing Musk argued that he would be denied a fair trial in San Francisco, where Twitter is based.

On Tuesday, the court reviewed the responses from dozens of potential jurors to a questionnaire, which included their opinions about Musk.

One potential juror acknowledged that he would probably not be impartial. "There's also the billionaire aspect. I'm not a big fan of those people," he said.

Alex Spiro, Musk's lawyer, asked those up for jury selection to remain "open-minded" even if they will first hear the version of the accusers.

He also asked the court to not bring up "recent events at Twitter."

After taking over the social media site in October, Musk fired more than half of its 7,500 employees and upended its content moderation policies, including unblocking the account of former US president Donald Trump.

"For the last several months, the local media have saturated this district with biased and negative stories about Mr. Musk that have fostered... highly prejudicial biases in the jury pool," the CEO's lawyers argued in a filing.