Whether you have to pay NY tax depends on why you are working in CT; whether it is for your convenience or the convenience of the employer, and whether you actually work in NY at any time. Don't be surprised if NY rejects your request for a refund. Please let us know, either way to help others with the similar situations.
For a long thread on this topic ,See
https://ttlc.intuit.com/community/state-taxes/discussion/re-i-work-for-a-ny-company-remotely-from-nc...
