UKJC:
The law for the DMV regulation exempting emissions testing specifically refers to " Composites " In CT, the DMV issues the VIN for Composites after the safety inspection, format is CT XXXXX
Since your make in NY is not a Composite and a 2006, the question may arise which is the best approach, register as a Composite with the inspection process etc or attempt to pass the emissions test.
The DMV transfer:
Requirements to Transfer Your Out of State Registered Vehicle. Go to the following link and click on Registration Services to the left, Transfer:
http://www.ct.gov/dmv/site/default.asp