No, the state return cannot be electronically filed before the Federal return. It must be either included with the Federal return and filed at the same time, or filed after the Federal return has been accepted. This adds a layer of security with your state return.
However, you can go ahead and electronically file both returns and get your state refund. Then pay the Federal balance due later. Even if you file your Federal return now, you have until April 15th to pay any taxes due.
See the following TurboTax help article for more information:
How can I pay my federal taxes?
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