I am wondering if I need to do anything further re: my CT state income tax refund? My dashboard indicates 'started' but I'm unclear if I need to do anything else?

[SteamTrain]

Probably means it cannot be filed at all yet...you've started it, but it hasn't been filed.

Check here yoru CT forms status (in the actual software) here:

Intuit App

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The CT tax returns cannot be filed until after 26 January...if yoru file contains the form CT-6251, then you have to wait until after 9 February to file

[ErnieS0]

Did you go through all the screens in the Connecticut section of TurboTax and run a state review? If not, make sure you do so.

If you did not, click on Your State Taxes in the right column, then tap Continue.

Tax champ @StreamTrain is correct. TurboTax expects Connecticut filing to be available on Jan. 26. 

You can use the link in @SteamTrain’s answer or check Connecticut Individual Form Availability for the latest updates.