What should I do if I receive a Post Filing Notice from my State saying I owe taxes. Turbotax e-filed my return. I was supposed to get a refund from my state (CT).

If you wish to dispute you must respond in writing with your evidence that your return is correct.

Otherwise, pay up.

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.

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/

Normally you will receive a letter of explanation from your state revenue office when they change or amend your tax return.

Connecticut's Taxpayer Assistance Number is 1-800-382-9463 if you would like to call.