There are a few different requirements for filling a CT tax return:
Who Is Required to File a Connecticut Return?
You must file a Connecticut resident income tax return if you were a resident for the entire year and any of the following is true for the taxable year:
If none of the above apply, do not file a Connecticut resident income tax return.
Gross income means all income you received in the form of money, goods, property, services not exempt from federal income tax, and any additions to income required to be reported on Form CT-1040, Schedule 1.
Gross income includes income from all sources within Connecticut and outside of Connecticut.
Gross income includes but is not limited to:
You must file a Connecticut income tax return if your gross income for the taxable year exceeds:
You can learn more here: http://www.ct.gov/drs/cwp/view.asp?a=1462&q=499520
I hope this helps!