State tax filing

It depends. Usually, when you register your vehicle as non-operational, you will only pay registration fees and there is no VLF assessed. The Vehicle License Fee (VLF) is the only portion of your fee that is tax deductible.

As shown below, the deductible VLF fee (License Fee) is listed separately from the registration fee. When you registered it as nonoperational, what fee what were you mandated to pay? If only the registration fee, then you did not pay a license fee. 

You can also use the CA VLF Fees Calculator to determine if you paid a license fee.