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The 19-year-old died after reportedly being crushed when hundreds of people tried to leave a party at Dundas St flat The Manor earlier this month.
Otago Coastal area prevention manager Inspector Wil Black said interviews had been completed and the case file would now be put together before being sent to the coroner.
It was still unclear if any charges would be laid.
"I think everybody acknowledges that party wasn't put on for any other reason than for those students to have a good time, and unfortunately that didn't happen on that night, and that tragedy occurred," he said.
"Once that file is complete, and the file is reviewed, then a decision will be made at that time. But I think the focus has been to make sure everybody was supported ... because you know, we don't want another tragedy coming out of what was already a tragedy."
About 20 officers were still working on the case and he did not expect it to take too long.
After reports that up to 600 people were at the party, Insp Black said that had been narrowed down to about 300.
A clean-up day in the student area was held last weekend, at the request of Miss Crestani's parents.