June 10 (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)