According to the CT Department of Revenue -
If you are a resident of Connecticut and you are required to include any part of the gain from the sale of the house or land (located in Connecticut or outside of Connecticut) in your federal adjusted gross income, that portion of the gain is also subject to Connecticut income tax. If you are a nonresident who sold a house or land located in Connecticut and you are required to include any part of the gain from the sale in your federal adjusted gross income, that gain is also subject to Connecticut income tax. However, if you are a resident or a nonresident selling your primary residence and you meet the federal criteria for excluding that entire gain from federal income tax, none of the gain will be included in federal adjusted gross income and will not be subject to Connecticut income tax.
So if you meet the federal home gain exclusion, you will not have any CT nonresident state filing requirement.
