Generally, your income tax is based on where you're physically located when earning the income. So, if your job's office is in state A, but because of the pandemic you're living and working full time in state B, you'd pay income and all other taxes to state B.
In this instance, you'd still be responsible for taxes for the period you lived in CT. You will file PY resident returns for each state and allocate the income received. You would also want to make sure you update your withholding information with your employer to reflect the move.
I hope that helps!
-Dennis
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