Mr Smith, 19, had a broken ankle and superficial head injuries.
White lost his bid to have his manslaughter conviction quashed by the Court of Appeal last year.
The Crown is now seeking to have his conviction used as "conclusive proof" that he was driving to convict him in relation to two other driving charges - driving while disqualified and driving with an excess blood-alcohol level - stemming from the same crash.
Police allege White was driving while disqualified and driving with an excess blood-alcohol level in the approximate range of 83 to 103 micrograms per 100 millilitres of blood.
At a special hearing in the Tauranga District Court, White's new lawyer James Maddox urged Judge Peter Rollo to exercise his discretion to allow "new defence evidence" to be tendered to the court and fully examined at a defended hearing which he argued would "show White was not driving".
Mr Maddox said White's family had engaged another independent crash investigator whose own findings differ significantly from the police evidence.
Judge Rollo has reserved his decision.