What do I do with my taxes check if my state taxes didn’t get taken out

What tax did you think was being taken out?   If you received a federal refund check, yes, you can cash it.  It is impossible to pay your state tax due from a federal refund, so the IRS would never take out the state tax you owed from your federal refund.  If you owed tax to the state, you are now late and need to pay the state by mailing the state a check or money order or by going on the state's website and using a credit or debit card to pay.

The “summary” given to you by TurboTax must have confused you.  That summary just nets out the difference between a refund you are getting and an amount you owe.   Or it adds two refunds or tax “due” amounts together.

The federal and state treasuries are completely separate from each other.  

Your state tax due cannot be paid from a federal refund.

And….your federal tax due cannot be paid from a state refund.  

Neither refund can be used to pay the amount due to the other one.

If you owe tax due, you have to pay it yourself by the filing deadline on April 15, 2024.

 If you have federal tax due you can pay by mailing your payment with the 1040V voucher, (which has the address printed on it, having the payment taken out of a designated bank account, or you can pay directly on the IRS website. 

https://www.irs.gov/payments

https://ttlc.intuit.com/community/tax-payments/help/how-can-i-pay-my-federal-taxes/00/26212

https://ttlc.intuit.com/community/tax-payments/help/how-do-i-pay-my-irs-tax-due-with-a-check-or-money-order/00/26403 

To apply for a payment plan with the IRS

Apply Online for a Payment Plan

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/questions/1901670-how-do-i-contact-my-state-department-of-revenue

First of all better double check if your state return was filed and Accepted.  When you efile you get back 2 emails. The first email only confirms the transmission. The second email says if the IRS (or state) Accepted or Rejected your efile. When you log into your account you should also see the status and if it was Accepted or Rejected, Started, Printed, Ready to Mail, etc. What does it say?

Check the printout or PDF of your return; look for the state cover sheet with the Turbo Tax logo. If you owed tax, it will show the payment information and how/when you decided to pay. Read the state payment instructions carefully since most states cannot be paid from within the TT system and requires additional steps.

Your only proof of payment is your bank statement or credit card showing the payment coming out. Turbo Tax only passes your bank account number to the state for the state to take it out of your account. But most states do not let you pay by Direct Debit so you have to mail in a check or go directly to the state's website to pay.