In 2021, I sold stocks at a loss in California before moving to another state by end of 2021. I still own a rental property in California that generates $10000 in income

[labrador2011]

On my California return can I deduct the allowed $3000 loss from stock against the $10000 income. 
I don't deduct it from another state as I live in a state that has no state tax

[MarilynG1]

Your $3,000 Capital Loss Carryover will reduce your income on your Federal return, which in turn reduces your California income.

Here's How to Enter a Capital Loss Carryover. 

For California, here's instructions on How to Enter Gain/Loss Adjustments. 

Here's more info on Capital Loss Carryovers in California.