Letby had been questioned in prison over baby deaths and "non-fatal collapses" at the Countess of Chester Hospital, where she worked, and Liverpool Women's Hospital, where she trained as a student Cheshire Police said on Wednesday.
Letby was interviewed "under caution", meaning the interview was recorded and can be used in future prosecutions.
The 34-year-old nurse was sentenced to life with no chance of release for killing seven babies and trying to kill seven others while working as a neonatal nurse at the Countess of Chester Hospital in northwest England in 2015 and 2016.
Prosecutors said she harmed babies in ways that left little trace, including injecting air into their bloodstreams, administering air or milk into their stomachs via nasogastric tubes, poisoning them with insulin and interfering with breathing tubes.
Detectives are reviewing the care of about 4000 babies admitted to hospital while Letby was working as a neonatal nurse.
Letby, who testified that she never harmed a child, has continued to proclaim her innocence and has tried unsuccessfully to appeal her convictions.
Some scientists and legal experts have questioned aspects of the circumstantial and statistical evidence used at her trial, and supporters have pushed for a review of the case.
A judge-led public inquiry is under way to examine failures by the hospital to recognise why babies were dying in the neonatal unit and to stop Letby sooner.Â
It is not reviewing Letby's convictions.
Dr Stephen Brearey, the senior pediatrician on the neonatal unit at the Countess of Chester Hospital, told the inquiry in November that Letby was likely to have murdered or attacked more babies before she killed her first known victim, a premature twin boy known as Baby A, in June 2015.
"On reflection, I think it's likely that Letby didn't start becoming a killer in June 2015, or didn't start harming babies in June 2015," he said.
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