Non-residents of CT are taxed by CT on Connecticut-sourced income. Scroll down to "Connecticut-sourced income of a Non-resident" in this CT tax publication for the details:
https://portal.ct.gov/DRS/Individuals/Nonresident-Part-year/Tax-Information#whomustfile
Note in particular that compensation for services is CT-sourced only if the services are carried on in Connecticut. Remote work carried on from a Florida location is carried on in Florida, not "in" Connecticut.
The general rule for sourcing of work income is that it is sourced where the work is actually (physically) performed. Otherwise (for example) every employee of Coca-Cola (headquartered in Atlanta) would be paying Georgia state income tax. Also, if Florida had an income tax, you'd be paying income tax to Florida - even though your employer is located in CT.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
