(Reuters) -California State Teachers' Retirement System (CalSTRS) became the latest investor to say it will vote against Tesla CEO Elon Musk's $56-billion pay package, the pension fund's chief investment officer told CNBC on Monday, days ahead of a consequential shareholder meeting.

The Thursday meeting will be a crucial test of Musk's leadership, particularly as investors have started to question the outlook for the electric-vehicle maker as sales have slowed and Musk attempts to shift its focus to achieving a breakthrough in artificial intelligence.

Musk is betting on a groundswell of retail investors to vote in favor of the pay package, the largest in corporate America, after a Delaware judge nullified the previous 2018 agreement, saying it appeared to be negotiated by a board of directors beholden to Musk.

So far, influential investor advisory groups Glass Lewis and ISS have weighed in against the new pay deal, and several institutions have also said they will vote against it.

Bernstein analysts said in a note on Monday that the package is unlikely to pass, as it would need a large percentage of outstanding votes to win investor approval.

"If the pay package were to be voted down, we believe it could increase uncertainty regarding the future leadership of the company and jeopardize the 'Musk premium'," CFRA Research senior equity analyst Garrett Nelson said.

The pay deal would give Musk roughly 20% control in Tesla, and he has argued he needs even more control. The pay package has no salary or cash bonus and sets rewards based on Tesla's market value rising to as much as $650 billion over the 10 years from 2018.

CalSTRS did not immediately respond to a Reuters request for comment. Norway's $1.7-trillion sovereign wealth fund said on Saturday it would vote against ratifying Musk's compensation package, while Baillie Gifford-managed Scottish Mortgage Investment trust said last month it plans to continue backing the pay package.

New York City Comptroller Brad Lander, who oversees public pension funds and fund consultant SOC Investment Group, is against the $56-billion compensation package and also said they were against the re-election of directors Kimbal Musk and James Murdoch to the board.

Tesla is also proposing to reincorporate in Texas instead of Delaware and re-elect two directors, including Musk's brother, Kimbal.

(Reporting by Akash Sriram in Bengaluru; Editing by Anil D'Silva and Shounak Dasgupta)