Ms Pucci-Love told an inquest into the death of Melbourne transgender woman Bridget Flack that three days after she went missing in late 2020, an officer informed her "no more could be done".
She tried to get police to search Ms Flack's Flemington flat, but was told to call firefighters "and just say there's been smoke".
Police did not conduct their own search for the 28-year-old, despite family raising concerns over her mental health and suicide risk, the inquest was told on Monday.
"I don't believe they (police) understood the level of risk," Ms Pucci-Love said.
"I remember saying, by nature she's more vulnerable in public - she's more vulnerable to assault, she's more vulnerable to violence in public - and I was just astounded that initially it wasn't taken seriously."
Instead, Melbourne's LGBTQI community rallied and began their own search for Ms Flack - printing posters, organising media coverage and spreading awareness about Ms Flack's disappearance - with about 6000 people joining a Facebook page.
Ms Flack was found dead on December 11, 2020 by two members of the LGBTQI community who were searching in bushland near Kew.
A detective admitted at the inquest "we should be doing better".
Coroner Ingrid Giles is investigating a cluster of transgender or gender diverse deaths including Natalie Wilson, Matt Byrne and Heather Pierard, who all took their own lives between 2020 and 2021.
Ms Pucci-Love said her sister's serious risk of suicide and vulnerability as a transgender woman was not taken seriously by Victoria Police.
"I think that when you've got a cohort who is, by data alone, more susceptible to suicide and harm from public, that there needs to be an overlay of that," she said.
Detective Senior Constable Dan Garside said he found Ms Pucci-Love's evidence hard to listen to.
"I wanted to sink into my chair, to be honest," he told the inquest.
"It's a sister trying to find her sister, we should be doing better than that."
He said police could have entered Ms Flack's property themselves instead of the fire brigade becoming involved.
"I think common sense applies with things like that, and you just do it ... They could've got through that door however they needed to," Det Sen Const Garside said.
Victoria Police Deputy Commissioner Neil Paterson admitted the search for Ms Flack was lacking.
"There are ways that the ground search for Ms Flack could have been managed a lot better, that should not have led to members of her community finding her deceased," he said.
Counsel assisting Gemma Cafarella made clear in her opening that the coroner was not making a link between identifying as transgender or gender diverse, and psychological distress or mental illness.
"The aim is instead to investigate the commonalities between these deaths and to hear from the experts to see if any prevention opportunities can be harnessed to avoid future similar deaths," she said.
The inquest continues.
Lifeline 13 11 14
beyondblue 1300 22 4636
Fullstop Australia 1800 385 578
21°C