You can.
Below is a TurboTax link on the subject.
Looks like you select that the W-2 is for Family Leave (taxable on the Federal return) and when you start the California return you will enter that amount so it will not be taxed by the state.
Since this was not paid by your employer but rather through the insurer, enter the full amount on the state screen. Paid through the insurer is similar to being paid though the state. This W-2 should suffice as a substitute for a 1099-G.
"When you indicate in TurboTax that the W-2 is PFL, a screen about PFL appears in the California section of the interview.
The amount of PFL wages on the W-2 is displayed, so you don’t have to look it up. However, you must enter the amount (if any) that was paid by an insurance company, and not your employer.
If none of the amount was paid by an insurance company, but all of it was paid by your employer, then you must enter zero ($0) in the wages box, because any amount reported by your employer in box 16 of a W-2 is considered by California as compensation for services or taxable fringe benefits."
TT LINK
According to the state of California:
"A Voluntary Plan (VP) is an alternative to State Disability Insurance (SDI). A VP must provide all the benefits of SDI and at least one benefit that is better than SDI, and it cannot cost employees more than SDI. An employer or a majority of employees can apply for approval of a VP to receive Paid Family Leave (PFL) and Disability Insurance benefits. For more information, visit Voluntary Plan Information."
CA LINK
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