Ms Lloyd had been living in Australia for about six years and worked in hospitality.
Queensland police launched a homicide investigation.
Inquiry head acting Detective Senior Sergeant Damon Mulcahy yesterday told the Bay of Plenty Times that Ms Floyd's partner had always been a person of interest.
"We have made a number of attempts to obtain a formal written statement from Melanie's partner about his version of events, but he has continued to invoke his right to silence, which he is legally entitled to do."
Mr Mulcahy said police had received good co-operation from family, friends, acquaintances and colleagues.
It had been established that Ms Floyd was off work for few days, and it was believed an incident had taken place at her home.
A post-mortem examination had been carried out on April 18-19 but police were still waiting for scientific results, he said.
Mr Mulcahy said police were almost at the stage where they would start preparing a report for the coroner about what had occurred and that would not change unless there were developments.
"It would be up to the coroner to decide whether an inquest is required," he said.
Mr Mulcahy said it was too early to say whether charges would be pending.
Ms Floyd grew up in Tauranga and went to Otumoetai College.
Her Australian friends described her as a "vibrant and very popular person" who left an imprint on the hearts of everyone she met.
They launched a fundraising campaign to help pay for her funeral and help her parents with expenses.
A family member living in Tauranga, who did not wish to be named, yesterday said Melanie's grieving parents - Bobbee and Bruce Floyd, who have been living in Queensland for about three years - preferred not to comment until police had finished their inquiries.
