New York and Connecticut are part of a Compact that allows NY to send the CT DMV information on your out of state speeding ticket. Now typically in Connecticut points are assessed if there is a conviction or bond forfeiture after a court hearing. Points are not assessed normally in CT if you make your payment in full and the case disposes at Centralized Infractions bureau.

Since the speeding ticket you received for 29 mph over the speed limit was received out of state, points may be assessed by the Connecticut DMV. You can contact the CT Driver Services division of the DMV for more information regarding points assignment for your NY ticket.

As for your insurance company, they will not be directly notified by New York about the moving violation. Instead once this offense is recorded on your CT driving record, your insurance company will be able to see it when they next pull your MVR.

According to the CT DMV, your driver's history will show if you have paid a fine for a motor vehicle infraction or violation or if a court found you guilty of such. Decisions about insurance rates and premiums are up to the individual insurance company and their rating system.