Although I can't endorse any particular lawyer's advice, this seems reasonable.
https://www.palmspringstaxandtrustlawyers.com/californias-4600-notice-request-for-tax-return-the-def...
If your father owns no property in CA, does not live in CA for any part of the year, and does not receive income from any CA source, then clearly this was triggered in error, simply because you are using your own address for your father's tax papers due to his age and health. In that case, a simple phone call to the FTB might clear it up.
If you do need to respond in writing, I would not send anything less than a fully executed form unless you have expert advice. And you would need to sign the form yourself and attach a copy of the power of attorney that gives you power over father's financial affairs.
