If you already completed (or are mostly finished with) your 2018 state return in TurboTax Online, go back into your state and look for a Need more time to file? or similar extension question or option, usually towards the end of the interview (step through your state again from the beginning if you didn't find it). Then follow the onscreen instructions in TurboTax.
Connecticut automatically gives you a 6-month extension to October 15 if you filed an approved federal extension and don't owe taxes on your Connecticut return. Otherwise, either print and mail Form CT-1040 EXT or file your extension online at their TSC online service by April 15. If you owe them taxes, submit payment by April 15 to avoid penalties. You can include a check with your Form CT-1040 EXT or pay online through the TSC online service.
Source:
https://ttlc.intuit.com/questions/1899449-do-i-need-to-file-a-state-extension-if-so-how-do-i-do-this