I filed by tax with turbotax electronically but later on have to amend it to fix it. But I haven't file my California state tax.

You can amend and add your state information.

 

  To amend your 2019 tax return: Wait to see if your return has been accepted or rejected by the IRS or state. If rejected, you can correct and re-send your return. If accepted you should wait until your return has been processed and you receive your refund or conformation that any tax due has been paid. If you file an amended return while you first return is being processed it can cause extended delays for both returns if two returns are in the system at the same time. In addition, if the IRS makes any change on your original return, you might end up having to amend the amendment. Amended returns can only be mailed - allow 8-12 weeks - can take up to 16 weeks (4 months) for processing.

 

How do I amend my 2019 TurboTax Online return? https://ttlc.intuit.com/community/amending/help/how-do-i-amend-my-turbotax-online-return/00/27577

 

To Amend on Windows. https://turbotax.intuit.com/personal-taxes/cd-download/amend/ty19/

My federal return has been accepted but still under processing. So you are saying, I should also file state return now and wait for the refund, then send amend of federal and state later?

Yes, you should wait until your returns have been processed, just in case there is a problem with your return that results in the IRS or your state proposing an adjustment (change).