Grace O'Malley Kumar, 19, was a medical student who was returning to her university with Barnaby Webber, also 19, when accosted by Valdo Calocane, who then went on to murder Ian Coates nearby.
The police watchdog has started an investigation into the Nottinghamshire force over its previous contact with Valdo Calocane before he killed three people last year.
Police are on the hunt for three machete-wielding youths who were spotted and recorded on CCTV in the early afternoon outside Nottingham art gallery on Friday.