The death of 10-year-old Milly Main at a children’s cancer ward at Queen Elizabeth University Hospital in Glasgow in 2017 is among those to be probed.
Police have been instructed by the Crown Office to investigate the circumstances surrounding the deaths of the four patients.
Scottish Labour leader Anas Sarwar, who has campaigned on behalf of Milly’s family for a full investigation, said the development was a “very welcome and overdue development”.
He added: “I have long argued that had this scandal occurred in the private sector, there would have been a criminal investigation.
“This is so serious it must be considered as corporate homicide.”
The QUEH opened in 2015 following a government spent of more than £840m but serious issues emerged surrounding the safety of its water supply, with a whistleblower first alerting that a child with cancer died after contracting an infection.
Milly was later identified as the patient. She was being treated at the Royal Hospital for Children, which is part of the QEUH campus, and had been in remission from leukaemia when her catheter became infected.
An independent expert panel reported earlier this year that her infection was “probably” related to the hospital environment.
The schoolgirl was one of 84 children who were infected with rare bacteria while undergoing treatment, with a third of them suffering a a severe impact on their health.
Parents have this month been speaking at the Scottish Hospital Inquiry, which is examining the construction of the QEUH campus in Glasgow and the Royal Hospital for Children and Young People and Department of Clinical Neurosciences in Edinburgh.
A spokesperson for the Crown Office & Procurator Fiscal Service (COPFS) said: “The procurator fiscal has received reports in connection with the deaths of three children and a 73-year-old woman at the Queen Elizabeth University Hospital campus, Glasgow
“The investigation into the deaths is ongoing and the families will continue to be kept updated in relation to any significant developments.”
A Police Scotland spokesperson said: “COPFS has asked Police Scotland to investigate a number of deaths at Queen Elizabeth University Hospital campus, Glasgow.
“Our investigation is at a very early stage, it would be inappropriate to comment further.”