I found this in the instructions for Form CT-W4:
Any nonresident who expects to have no Connecticut income tax liability should choose Withholding Code “E.”
https://portal.ct.gov/-/media/DRS/Forms/2022/WTH/CT-W4_1221.pdf
I would just enter "E" on Line 1 of the form.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
