Your only proof that you paid the state will be your own bank/credit card records.
I RECEIVED A LETTER FROM THE IRS/STATE
TurboTax does not receive any information from the IRS or your state after your return was filed, so no one at TurboTax knows about a letter you received from the IRS or the state.
I AM BEING AUDITED
If you purchased Audit Defense:
https://ttlc.intuit.com/questions/2924451-i-bought-max-or-audit-defense-and-now-i-m-being-audited
AUDIT SUPPORT
TurboTax has a special phone number for help with IRS/state tax letters, which will be easier than going through regular Customer Support. At the page below, click on the blue button that says "Get Help from TurboTax Support". Then it will ask you what tax year is your letter. Then it will ask you what the letter concerns. Then it will show you the phone number during posted business hours.
https://support.turbotax.intuit.com/irs-notice/audit-support/