Dozens of patients who had tested positive for Covid-19 were transferred from Scottish hospitals to care homes, a report has revealed.
Public Health Scotland (PHS) said 78 such patients were discharged to care homes between 1 March and 21 April.
Only 650 of the total 3,599 elderly patients discharged from hospital during the period had been tested.
Nicola Sturgeon, however, said there was "no statistical evidence" hospital discharges led to care home outbreaks.
The analysis found the size of care home played a bigger role, with the largest much more likely to have outbreaks than smaller ones.
Deaths in care homes account for about half of Covid-related deaths in Scotland, with about 2,000 resident deaths.
The first minister has previously said she only became aware from media reports that Covid-positive patients had been sent to care homes.
Quoting from the PHS report at her daily briefing Ms Sturgeon said: "The analysis does not find statistical evidence that hospital discharges of any kind were associated with care home outbreaks."
But she added: "Nothing in it detracts from the tragedy of the deaths that have occurred in care homes over the course of the pandemic, and nothing ever will detract from the heartbreak of those bereaved."
The delayed PHS report said nearly 5,000 individuals were discharged from NHS hospitals to care homes until the end of May, and about a third of care homes have had Covid outbreaks.
Of 78 patients discharged before 21 April after having had a positive test result, only 10 had been retested and found to be negative prior to discharge.
But the analysis found the biggest link in outbreaks was the size of the home itself - with possible factors including greater movement of staff at the larger homes, or a higher average age of residents.
It found that more than 90% of homes with more than 90 residents had an outbreak, compared to under 4% of homes with fewer than 20 residents.
While there were some indicators that suggested hospital discharges did increase the risk of an outbreak, the study was relatively small in statistical terms and the authors found no "statistically significant" evidence.
Health Secretary Jeane Freeman: "The data from this report gives us a better understanding of the impact of discharges on outbreaks in care homes.
"We will be taking forward the recommendations that PHS make in their report, and we will continue to adapt our guidance and the steps we are taking to protect care home staff and residents."
The Scottish government introduced a new policy on 21 April that required patients to have two negative Covid tests before leaving hospital, and all new care home admissions to be isolated for 14 days.
The report said a further 1,605 hospital discharges took place after this date, and 93% were tested in line with clinical guidance.
However, another 45 patients were discharged to care homes having had one positive test but without a second test result to confirm they were negative.
The report noted there were valid clinical reasons for not testing some individuals prior to discharge such as "capacity to consent to testing and avoiding causing distress, and to appropriateness of testing" - for instance in cases of end of life care.
'My mum had more living to do'
For relatives who lost elderly loved ones in the early weeks of the pandemic today's report does little to answer their questions.
Jackie Marlow's mother, Helen McMillan, died during an outbreak at a care home which she's convinced began when another elderly woman was discharged from hospital, developing a cough and later dying with suspected Covid.
This resident was one of nearly 3,000 hospital discharges at the time who were never tested, so the uncertainty remains.
"That's not her fault, it's not her family's fault - they lost her too," says Jackie.
"Had she been kept in hospital, had she been tested then maybe she'd still be here today because maybe she would have got the treatment that would have kept her alive - and my mum would still be here today."
She says there was no offer of her mother being transferred to hospital or getting oxygen. Visiting was suspended at the time and she was unable to be with her mother to hold her hand.
"They say it was unprecedented times - but does that mean because you're old you don't matter anymore, you don't count. It's horrific - my mum had so much more living to do."
Rodney Laing said his 80-year-old father, Rodger, was handed a "death sentence" when he was moved from Midlothian Community Hospital to a care home in May.
The dementia patient caught Covid and he died 22 days after moving into the home.
His son told BBC Radio Scotland's Drivetime with John Beattie: "He was fit and healthy, within three weeks and one day he passed away, he had to die alone with a bunch of strangers. It was just terrible."
Dr Donald Macaskill, chief executive of Scottish Care which represents private sector care homes, said the report was a "robust statistical analysis" but did not "tell the whole story".
He said: "The whole story can only really be told, and to be fair the report acknowledges this, when we talk to people at ground level - that's the staff, the managers, the operators of care homes - to see what their experience is.
"Behind each statistic there is a human story and behind each incident and outbreak there are the experiences of staff, some of whom are convinced in some cases that the infection arrived in the care home as a result of discharge.
"That's a minority but we need to hear that story and need to hear that as part of the evidence."
He repeated his call for a "human rights-based inquiry" into the experiences of care homes during the pandemic.
Opposition politicians said the report highlighted grave failings and called for ministers to be called to account.
Scottish Conservative Holyrood leader Ruth Davidson said: "The SNP government's response to this report is wholly inadequate and will give little comfort to those grieving families still trying to find out how and why their loved one died.
"Thousands of patients were transferred without a test and over 100 people, who were known to have coronavirus, were sent to care homes alongside some of the most vulnerable people in our society."
For Scottish Labour, Monica Lennon said: "The decision to move patients with Covid-19 into care homes was reckless and SNP ministers must be held to account for this Russian roulette strategy.
"The combination of knowingly transferring the virus into care homes and not bothering to test hundreds of other patients before moving them, is unfathomable."
Scottish Greens health spokesperson Alison Johnstone said the "scandal" had been known for some time but the scale of it was "astonishing".
She said: "Care homes are supposed to be safe havens for some of the most vulnerable people in our communities and it is an absolute tragedy that so many people have been fatally let down in this way.
"That so many families have lost a loved one due to systematic policy failures is an appalling reflection on the handling of this crisis."
And Willie Rennie, leader of the Scottish Lib Dems, said: "Our care homes had a monumental challenge keeping residents safe from the virus but the government made that task even harder by failing to stop people with the virus from entering the homes and not even finding out if thousands more had the virus.
"It's easy with hindsight to see the sense in testing all people before admission to care homes but you don't need hindsight as I warned the first minister repeatedly at the time."