CT considers that CT source income* (many states do not). You have to file a non resident CT return. SC also taxes unemployment compensation, so you have to report it on your SC resident return. But SC will give you a credit (or partial credit) for the tax paid to CT.
*Reference: https://portal.ct.gov/DRS/Individuals/Individual-Tax-Page/Unemployment-Compensation#:~:text=Nonresid.... "Nonresidents must file Form CT-1040NR/PY and report the unemployment compensation, along with any other Connecticut source income, on Schedule CT-SI of that form."
