Massachusetts is not a member of the Drivers License Compact but the MA Registry of Motor Vehicles (RMV) has agreements so that they still are able to share information regarding tickets with other states and receive out of state citation information for their motorists. So likely your DC "no left turn" ticket will be reported to the MA RMV.

It would appear from the RMV information that most offenses committed in other states will be put on your Massachusetts driving record and treated by the Registry of Motor Vehicles as if it occurred in state.

If MA does treat it as if the violation was incurred in state than you would likely be assessed a 2 point insurance surcharge for this minor traffic violation. This is according to the SDIP surcharge listing.

If you do not pay or take care of your DC ticket in any way, your driver's license will likely be suspended. Massachusetts and DC are both members of the non-resident violator compact.

This compact requires states taking part in it to suspend the driver's privileges of a person who gets a traffic ticket for a moving violation in other states and fail to pay them. So DC would notify MA of your failure to take care of the ticket and then MA should suspend your license.

For more information on if out of state tickets will affect your insurance rates try contacting the Massachusetts Division of Insurance.