You will have to print and mail your Arkansas state tax return, unfortunately, if you are a first-time filer in the state.
This is not a TurboTax restriction, but rather it is a function of Arkansas state law. When you are a second-year (and subsequent) Arkansas income tax filer, then you will be able to e-file your state return, along with your federal return (which you can e-file even if this is your first year).
Please see the screen-capture picture image attached the bottom of this message for details (simply click to enlarge).
Thank you for asking this important question.