Apparently, Turbo Tax will not e-file an amended state return if the federal amended return cannot be e-filed. This should be stated in the e-filing module.

TurboTax can't e-file any amended returns, even if you live in a state that allows it. Amended returns need to be printed and mailed in. Or, if you live in the state that allows amended returns to be e-filed, you would have to print the return from TurboTax, and transfer the information to your state's online self-filing system. 

Amended returns cannot ever be e-filed.  Ever.  Amended returns must be printed, signed, and mailed.  When you print out the return, there will be filing and mailing instructions as to where to mail it.

Thank you.  TurboTax needs to correct the program since it prompts me to e-file an amended state return.