Please verify your W2 form issued by your employer - does it reported your income taxable in NY - lines 15, 16,17?
Does your W2 form reports your income as taxable in CT also?
If you filed CT income tax - I suggest you to mail a copy of that return to NY as a proof that you did not have was not a resident of NY.
Do you have NY driver's license? Do you own any property in NY?
I would suggest also to contact NY DOT and find out the exact reason your claim for refund was rejected - http://www.tax.state.ny.us/nyshome/telephone.htm
Based on information given - you are not responsible for NY income tax.
As you do not know the actual reason why NY DOT rejected your tax return and denied your refund of NY income taxes - your first step would be to clarify that issue.
In such situation - I would sent the letter asking for clarification and to reconsider their decision. Please attach a copy of your CT tax return, copy of CT driver's license, letter from your employer that states your workplace is in CT, etc.
I hope you will be able to resolved your issue.
If they would still deny your claim - you likely will need a local CPA or Enroll Agent to represent you.