What type of helicopter is shown in Star Wars The Last Jedi featurette?
The helicopter is a Eurocopter EC135 T2+. The registration (just above the tail rotor) EI-ILS shows that this aircraft was registered in Ireland, this helicopter was sold to PDG HELICOPTERS in early 2016 and is now on the U.K. register as G-GLAB. Based on this information it suggests that this particular segment was filmed before or shortly after early 2016 when the aircraft would likely have been re-painted with the new registration.

Eurocopter are a popular "household name" in aviation with numerous models operated throughout Europe and beyond in various roles such as airborne policing, medical flights (air ambulance), and some military operations. Eurocopter now operate as "Airbus Helicopters" and subsequently the EC135 has been re-designated as the H135.