"do we need to add the CT Tax withholding amounts from the W-2 back?" - no
"The answer is still very confusing, please clarify." - yes, it is confusing. The state of Connecticut starts with the federal AGI - Adjusted Gross Income. However, this number may contain some Connecticut tax that you have deducted on the federal real. Connecticut does not want you to leave that deduction in the AGI in the state return, UNLESS that state tax was in Itemized Deductions (Schedule A) (which they specifically allow). As the example says (in the Learn More in TurboTax), if you you deducted any state income tax on your Schedule C (self-employed), you would need to add that back to the AGI.
Really, this does not apply to most taxpayers, so if you haven't paid any CT state income tax for any reason besides to go on Schedule A, this does not concern you.
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