Normally you will want your vehicle registered and insured in the same state, the state in which you reside and the car is garaged. There may be some instances where you can have your car registered in one state and insured in another, such as you are a permanent resident of one state but go to school in another and have insurance there, but not all states or insurance companies allow this.
New York is one state that does not appear to allow such a scheme. The New York Department of Motor Vehicles site states that they do not accept any out-of-state insurance documents.
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For vehicles registered in New York State the liability coverage must be NYS insurance coverage, issued by a company authorized to do business in NYS and licensed by the NYS Insurance Department. Out-of-state insurance coverage of any type is NEVER acceptable or valid.
The DMV again reiterates that if your vehicle is registered in NYS, the liability insurance coverage must be NYS insurance coverage. So it appears that NYS would not allow you to place insurance from Connecticut on your New York registered vehicle but that you must have car insurance issued by a NYS insurer.
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