Normally, TurboTax asks you to add a state return, based on where you say you live, and state withholdings indicated in boxes 15-17 on your W-2. In addition, there are much less common places that would indicate that you might owe tax to a state other than where you live.
Based on these entries, TurboTax would normally ask you if you want to file a state return. Even without this, as Mike notes, most state interviews also ask you if you made money in another state, even though there was no flag to trigger TurboTax to add the state.
I have to wonder, though, if the notice from the CA Franchise Tax Board is correct. Why do they think that you should have filed a CA return? Did someone send them a tax form that referenced CA? Did you formerly live in CA in 2020 but move out, but the state didn't notice? Please note that "domicile" (residency) once determined is not changed until you take positive steps to show that you have changed your domicile; this means that CA thinks that you owe them a return until you prove that you changed your domicile.
So what kind of return does CA want, resident or non-resident?
In any case, since they sent you a notice, you should reply to them asking what type of return they think that you should file and why. Their justification might be quite enlightening.
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