California Capital Loss Carryover

Yes, California also allows capital loss carryovers. 

Unlike the federal government, California makes no distinction between short-term and long-term capital gains. It taxes all capital gains as income, using the same rates and brackets as the regular state income tax.

See the California Instructions for Schedule D for more information. Near the end of the instructions is the "worksheet" for capital loss carryovers:

California Capital Loss Carryover Worksheet

1. Loss from Schedule D (540), line 11, stated as a positive number.
2. Amount from Form 540, line 17.
3. Amount from Form 540, line 18.
4. Subtract line 3 from line 2. If less than zero, enter as a negative amount.
5. Combine line 1 and line 4. If less than zero, enter -0-
6. Loss from Schedule D (540), line 8 as a positive number.
7. Enter the smaller of line 1 or line 5.
8. Subtract line 7 from line 6. This is your capital loss carryover to 2023.

When you prepare the California return in TurboTax, at the screen "Here's the income that California treats differently", under Investments, you can click on the item "Capital Loss Carryover from Last Year" and make any needed adjustments.