Your daughter's Form W-2 information has nothing to do with the Connecticut income tax adjustment you referred to in your initial post. As far as the adjustment issue goes, disregard her W-2.
As LenaH indicates above, your daughter should only enter an amount in the Connecticut income tax adjustment field if she deducted Connecticut income tax anywhere other than on Schedule A on her federal tax return.
If she didn't do this, she doesn't need to worry about the income tax adjustment.
See Line 37: Other in the Form CT-1040 Connecticut Resident Income Tax Return Instructions for more information.
