It's unclear what you mean.
If you are using the Desktop version of Turbotax (installed on your own Mac or PC), there is a $25 or $30 fee to e-file your state tax return. (There is no extra fee to e-file a federal return.) Yes, you can print your state return and mail it in, and avoid the extra fee. Even if you print and mail your state return, you can still pay your tax owed from your bank account, or get a direct deposit of your refund into your bank account. Your bank account numbers will be printed on the tax return and the state will get the information that way.
If you are referring to the $40 extra free for refund processing that applies to a federal return, that is only if you want to pay your turbotax online fees by deducting them from your refund. If you pay your program fees with a credit card, you won't be charged this extra fee when you file, and it won't be deducted from your federal refund if you are expecting one.
No matter which version of Turbotax you are using (desktop or online) there is no extra fee to e-file your federal return, or to have your refund directly deposited into your own bank account without deductions.
