I would stringly suggest that a DI would not be involved in a pursuit as they wear plain clothes and drive ordinary unmarked cars. Traffic officers have both marked and unmarked vehicles, the unmarked have hidden blue lights etc.
A marked vehicle normally transfers the accused to the station but in the case you say the person has suffered injury and would deffinately be taken to hospital in an ambulance for treatment, once at the hospital they would be de-arrested and bailed to attend the station at a later date, if drink or drugs were suspevted then the police have the power to take blood at the hospital.
Hope this helps
Alan (14yrs service)