You really haven't provided any information to work with. Are you a CT residence? Is the mlitary member a CT residence? Is the military member currently stationed in CT? Is the non-military spouse with the military member on PCS orders for whatever place they may be stationed at?
Please see https://portal.ct.gov/DRS/Individuals/Individual-Tax-Page/Income-Tax-Information-Military
There are three sections.
1. Personnel whose home of record is Connecticut
2. Nonresidents whose home of record is outside of Connecticut
3. Military Spouses Residency Relief Act
If both the military member and the spouse are not CT residents (as shown on the military member's LES statement in the "STATE" box), then I would expect the MSRRA to apply and you can follow the directions provided on the aforementioned website to get any withheld state taxes refunded, as well as make the state's tax assessment on your income "go away".
