For your individual tax return, you don't enter your CT K-1 in the program. Your Federal K-1 will flow to your state return. If you are a CT resident, you would use the CT K-1 as a reference to make necessary adjustments to your CT return in the interview, on the screens Here's the income that Connecticut handles differently and Take a look at Connecticut credits and taxes.
If you are a nonresident, you will allocate the portions of your income and expenses that are sourced in CT.
I am referencing TurboTax Business. The income from my federal Form 1065 pg 5-6, is not transferring correctly to Page 1 of my Connecticut State Form 1065. Is this a known issue?
TurboTax Business does not yet support the new CT-1065/CT-1120SI forms nor does it support the Pass Through Entity Tax and new CT-PET form. (Form CT-1065/CT-1120SI has been changed from the Connecticut Pass-Through Entity Tax Return to the Connecticut Composite Income Tax Return.)
The new CT forms rollout has caused delays and CT pushed its filing deadline to from March 17 to April 15.
TurboTax has not provided an answer as to whether they will support the new CT forms in the coming days - you may need to file directly through myconnectCT.