The boy, who was visiting from the UK, remains in a critical condition in Southampton Hospital.
Officers have taken statements from a number of witnesses to the crash, which happened about 4 pm near the Millennium Town Park, but would like anyone who left the scene before being speaking to the police to call the station on 612612.
Police are also requesting that anyone who has premises in the area with CCTV cameras get in touch so footage can be viewed to see if it assists with the investigation.
A 38-year-old woman has been arrested for traffic offences after hitting the toddler, and has since been released on bail.
The police are also offering guidance for anyone traumatised by the accident: “A range of support is available for anyone who may have been distressed as a result of this incident,” they say. “GPs will provide support on emotional health and wellbeing concerns, while other options include the Youth Enquiry Service, school-based counsellors, the Samaritans and – in cases of appropriate seriousness – the Emergency Department at Jersey General Hospital.
Meanwhile, another visitor from the UK, a 73-year-old man, is still in hospital after the car he was driving crashed into railings at the Harbour yesterday afternoon.
The entrance to the Elizabeth Terminal was closed off for a period after the crash, which happened just after 1 pm. No other cars were involved and the entrance to the Terminal later partially opened to let vehicles and passengers through to board a ferry.
The man was treated at the scene by paramedics before they took him to A&E. The Health Department say he is currently in a stable condition.