He unleashed a knife rampage in Nottingham last year, killing two 19-year-old students and a 65-year-old man before driving a stolen van into pedestrians.
He was given a hospital order last week for their manslaughter.
Now, Leicestershire Police has referred itself to the IOPC over its investigations into alleged assaults by Calocane in May 2023, just weeks before the killings.
“Following the sentencing of Valdo Calocane several incidents involving previous police contact with him have been brought to our attention which we were unaware of,” the IOPC said.
“As a result, we asked Nottinghamshire Police and Leicestershire Police to provide us with information promptly about those incidents to establish whether there are any matters that should be referred to us.
“We have this afternoon received a referral from Leicestershire Police about its investigation into assaults Valdo Calocane was alleged to have committed on May 5 2023, which we are assessing to determine what further action may be required from us.”
Calocane killed Barnaby Webber and Grace O’Malley-Kumar as they walked back to accommodation in Nottingham early on June 13.
He hacked Barnaby to death and Grace was killed as she bravely tried to intervene to save her friend.
Calocane tried to break into a homelessness hostel after, but was fought off, so he instead killed Ian Coates, a school caretaker, and stole his van.
He drove into three pedestrians, all of whom were lucky to survive, before being boxed in by police and Tasered.
The IOPC said Nottinghamshire Police had also contacted it about Calocane.
“In relation to a warrant being issued for Mr Calocane’s arrest in 2022, Nottinghamshire Police provided us with information about that shortly after the tragic events of June 13 2023,” a statement on Monday said.
“We decided it did not meet our referral criteria because the contact had not been recent and no conduct issues were identified for any individual officer.
“Nottinghamshire Police subsequently carried out an internal review of matters linked to the warrant and we have now also requested details of that learning exercise, in case there are any issues that would require our involvement.”
It comes after relatives of the victims criticised his hospital order.
He was deemed to have paranoid schizophrenia, but families fear they will live in fear he will be let out one day and have called for an inquiry.
They met Rishi Sunak at Downing Street on Monday, along with home secretary James Cleverly, justice secretary Alex Chalk and health secretary Victoria Atkins.
“We did get an assurance from the Prime Minister himself that if it’s required, they’re not ruling out a public inquiry (into the attack), and they will do a public inquiry,” he said outside No10.
