When you have an automatic and you drive in D, you cannot really overspeed. If you drive to fast for a gear, even kickdown will not shift back to that gear. You can overspeed if you put the selector in S or L when driving to fast.
With a manual gearbox it is also possible to overspeed, certainly when downshifting. The governor will limit the speed when you stay in a gear, but that speed will be higher than the speed of maximum power. So if you are in second gear for instance and you press the accelerator, the car will go above 37 mph, until the engine reaches somewhere above 5000 rpm, while 37 mph is about 4400 rpm.
The older diesel, with a vacuum controlled governor, could not go above about 4200 rpm.