The police will have absolutely no role to play in this investigation, State or Federal. The Australian Transport Safety Bureau will be running this investigation from the beginning, as per Annex 13.
Let's not read too much into this aspect. The police DO have a role to play. When a Aerodrome Emergency Plan is activated, especially at a non-controlled aerodrome, the police take the coordinating role for the full 'ground response'. They will always 'report/investigate/wrap up any such "event" where they have a major role.
ATSB, who would have been notified by ATC long before the acft landed, will of course conduct the 'aviation investigation' of the actual occurrence itself.