Savannah Keenan, five, who lived at the Heath Common caravan park on Doncaster Road, Wakefield, suffered head injuries in the incident after she was hit by a red transit van.
The driver of the van, Gerald Johnston, 22, did not realise he had hit the girl and drove off unaware and without stopping, an inquest in Leeds heard.
In police interviews he said he had heard a noise but thought somebody had thrown something at his van.
PC Philip Eastwood, who investigated the accident, which happened last August, told the hearing that CCTV footage backed up Mr Johnston’s version of events as it showed him driving on with no sign of hesitation or panic, reiterating his claim he had not realised what had happened.
A police investigation has taken place but the Crown Prosecution Service (CPS) had decided no charges would be brought.
One witness claimed he had seen Mr Johnston look down as he was driving and when asked about this in police interview he did not comment, thought to be based upon legal advice. However investigations revealed Savannah had run out into the road from behind or in front of a parked vehicle and Mr Johnston would have had very little time to see her.
“It is probable that even if the driver had seen the child there would have been insufficient time to avoid the collision,” Robert Crispin, accident investigator, with West Yorkshire Police said.
The hearing was told when Mr Johnston, who had just left his wife’s caravan at the site shortly before the accident happened, heard of the crash he returned and made himself known to police.
There were speed humps on the road and police said Mr Johnston was not speeding at the time of the accident. Tests showed he was travelling at a speed of just over 12mph.
Savannah was taken to the accident and emergency department at Pinderfields Hospital, in Wakefield, but her death was confirmed minutes later.
A post-mortem concluded that Savannah had died of a head injury.
Savannah, who was born in Derby, lived with her parents Michael and Dawn at the caravan park.
Her parents did not attend yesterday’s hearing but in a statement her mother described her daughter as: “a beautiful, little girl.”
Recording a verdict of accidental death, coroner David Hinchliff, said the likelihood was that Savannah was not seen by Mr Johnston, who was visibly upset at yesterday’s hearing, and if he had seen her he would not have had time to react.
Heath Common is an authorised, permanent encampment managed by Wakefield Council.