Connecticut and New York are both members of the Drivers License Compact (DLC) so the New York State Department of Motor Vehicles will be informed of this speeding offense in CT since you plead guilty and paid the fine to Connecticut.
The NYS DMV has decided not to record out of state violations committed by New York licensed drivers except for in certain alcohol or drug related violations or moving violations that took place in Quebec or Ontario, Canada. Except for violation convictions coming from Quebec or Ontario, points are not added to a NY driver's record for out of state citations either, which is good since normally 15 mph over the speed limit is a 4 point offense in NY.
Since the Connecticut speeding ticket will not be placed on your NYS record it is unlikely, but not impossible, that your insurance rates will not be increased due to it. Your insurance company may be able to do a comprehensive search and see this CT speeding ticket. If that is the case, then it will depend upon your insurance company's rating system if your rates will go up.
You can find out about your carrier's rating system ask your agent or contact the NYS Department of Insurance since rates much be filed with this insurance regulatory body. For a New York car insurance quote click here.