You did not mention why you are amending your returns, but if you made a change that affected both your Federal and state returns, then you should file them both. If the change only affected your state return (such as correcting state taxes withheld) and had no bearing on anything on your Federal return, then you do not need to file the Federal amended return.
Your state balance due from the amended return will need to be postmarked by the due date of the tax return, not processed and accepted by the due date. Since the tax deadline has been extended to May 17, 2021, the due date for your state may have been extended as well. You can use the TurboTax article below to look up your state to see if the due date has been extended.
State income tax deadlines
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