Should I fill California state tax return if I have $0 state refund?

the issue is do you have a filing requirement regard of whether you owe or not or are due a refund or not

who must file

https://rlsglobalconsultinggov.com/help/who-must-file-california-income-tax-return-solution-found.html 

Filing requirements are not determined by whether or not you are due a refund.  “California filing requirements is based off of filing status, age, California gross income and California adjusted gross income.  See the filing requirements on the California Franchise Tax Board's website:

What are California's Filing Requirements?