Possibly. You must pay a CA minimum franchise tax of $800 by the 15th day of the 3rd month after the close of your tax year (usually March 15th).
Then, if your CA taxable income exceeds what that minimum $800 covers, you must pay other estimated tax payments.
Here is some more information about it.
Remember, there is also a Statement of Information that must be filed with the CA Secretary of State.
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