I'm not sure what the table at your link is supposed to indicate but the entry for 3582 in the "E-file" column is "unsupported". The entry in the "Print" column is "available" but the 3582 form doesn't appear in my return using either the "E-file" or "File by mail" options in the "File a return" step.
I'd already found the form on the California FTB website but was hoping the "unsupported" status in TurboTax was an error and not their policy going forward. I mean, if they can provide one for Illinois returns what's keeping them from supporting California?
