Sergeant Sheldon Kindley said it was too early to speculate on the laying of charges.
''There's quite a lot of work to be done,'' he said.
''We are doing our level best to get things done as accurately and timely as we can.''
Police were yet to interview all the occupants of the Laser, he said.
Two of the Laser's occupants remained in hospital yesterday - one with serious facial injuries which required further medical treatment and the other with minor upper body injuries, who was due to be released in coming days.
Tributes have continued to flow for Miss Strange.
A group gathered outside Miss Strange's Invercargill home yesterday.
Miss Strange's mother, who was visibly shaken, told the Otago Daily Times she was not ready to speak about her daughter yet.
Dozens of tributes were posted online.
''Rest easy beautiful lady. Fly high, you are gone but not forgotten, i love and miss you hun xxxxx,'' one tribute to an online page opened in Miss Strange's honour said.
The 18-year-old allegedly driving the car also took to social media to defend himself.
''Just so you all know, it was a f***ing accident,'' a post attributed to the 18-year-old said.
''I f***ing regret even getting in the f***ing driver's seat. I'm sorry everyone, it should have been me not Nakita.''
A police spokesman said the Laser failed to give way and was hit by the Courier, which was being driven up Stafford St, about 2.15am.
The driver of the Laser fled, but was found by police nearby, he said.
The driver was assisting police with their inquiries.
A death notice published in the Southland Times yesterday paid tribute to Miss Strange as a ''dearly loved daughter and friend''.
The notice said the ''loved'', ''cherished'' and ''adored'' teenager would be ''sadly missed''.
