Massachusetts has arranged to share driving records with other states so certain traffic offenses you have committed in other states will be placed on your driving record and treated by the MA Registry of Motor Vehicles as if they occurred in-state. The MA driver's manual does not state what exact out-of-state offenses they record on your driving record. You should check with the RMV to find out if the NY ticket will make it to your record or not.
We try to provide as much information as possible, but in some instances the answer is unknown. MA is very secretive and/or incompetent with their driving record information. When you speak to the RMV (not the Insurance Department) they will tell you that it is shared, but we have not seen any claims where it was shared.
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It is possible that a moving violation, such as a speeding ticket, could make your insurance rates go up but it is not a given. Each insurance company has its own guidelines to what makes them raise rates. You can check with the Massachusetts Division of Insurance with whom your insurance company must file their rates with.