Technically, yes. But, it would be very cumbersome. You would have to create an account and completely redo your Federal return exactly how it was filed by someone else. This is because TurboTax prepares your state return by transferring the information from your Federal return.
Also, you would not be able to e-file your state return due to safeguards that require a state e-file to be associated with a federal e-file in the same account. This means you can prepare your return online, but you would have to print and mail.