What tyre track dimensions can be measured at a crime scene and how could this help identify the responsible vehicle\?

It depends, but in the best case, one could obtain overall track width as well as number and spacing of tread blocks. Overall track width is a function of the vehicle geometry, and pretty difficult to alter, while tread block spacing could have course vary significantly from tyre to tyre.

This is generally pretty inconclusive when it comes to finding a particular vehicle, but would certainly be useful corroborative evidence if a particular vehicle was already suspected. It's probably more useful in ruling out a particular vehicle. In some very rare cases, one might have such a unique combination of tyre and axle characteristics that a particular vehicle would be indicated - but I wouldn't hold my breath.