TurboTax will automatically fill this form out for you based on the answers you provide in the state portion of the interview in the program. The online version of the program does not have an interface that allows you to go directly to the form itself.
If you're in the Online version you will select the STATE tab and add a state. Type in CT and go through the questions. It will ask for dates that you resided there, and what your status is. You will select Part Year Resident.
You can e-file or mail in your Form CT-1040NR/PY. TurboTax will give you both options in the File section. Connecticut income tax is based on federal adjusted gross income (AGI). If you e-file federal you should e-file CT-1040NR/PY.
If you mail your federal you will have to mail CT-1040NRPY. You will not be able to e-file Connecticut if you mail in federal.
TurboTax suggests e-filing federal and state together.