No, your state tax will not be deducted automatically. Your federal refund is never used to pay the state.
You must pay your state tax due using the state’s preferred method of receiving payment. For most states that will be by making a payment to the state’s own tax website, or by mailing a check or money order.
https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/contact-state-department-rev...
WHAT IF I CANNOT PAY MY TAX DUE?
https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-payments/pay-taxes/L8aQBCpPO_US_en_U...
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