Your home state of Connecticut and the state in which you were cited for speeding, New York, are both members of the Drivers License Compact (DLC) meaning that if you are convicted of the speeding offense by the NY courts they will inform the CT Department of Motor Vehicles.
The CT Department of Motor Vehicles typically assigns points to a person's driving history if they are convicted of a violation but not if you make a payment in full and dispose of your case. The CT DMV stated to us that if you hold a Connecticut Commercial Driver's License (CDL) then the violation would appear on your Connecticut record.
However if your license is a regular passenger car driver's license, Connecticut will not place the out of state violation to you CT record or assign points. The only time Connecticut would take action on this violation is if you do not pay the ticket and NY ticket and then the New York State courts contacted the CT DMV and requested them to suspend your license for non-payment or failure to comply with the speeding citation.
Since the CT DMV should not place the NY speeding violation on your Connecticut driving record it is doubtful that your insurance company would find out about this moving violation conviction and thus it would not likely affect your rates.
If your rates are somehow affected or if you just want to shop around for better premiums, get discount auto insurance rates quotes here.