An independent inquiry has cleared police officers of any blame in the run-up to the death of tragic Violet-Grace Youens.
The four-year-old was knocked down in Prescot Road, St Helens, last March by motorist Aiden McAteer and died from her injuries two days later.
Violet was with her grandmother Angela French, from Golborne, who was also seriously injured and spent weeks recovering in hospital.
Before the collision an alert had been issued by police regarding McAteer, who was driving a stolen Ford Fiesta with false number plates.
An officer trained in advanced driving techniques, Pc Neil McEwan, saw the car coming up behind him on a roundabout, according to the Independent Police Complaints Commission (IPCC).
He took the first exit, turning left and activated his blue lights, says an IPCC report, while the car continued onto the roundabout and took a different exit.
Pc McEwan performed a u-turn, returned to the roundabout and drove off in the same direction he assumed the car had gone.
Around one mile further down the road he arrived at the scene of the accident in which Violet-Grace was killed.
Alex Hall, the IPCC's lead investigator in the case, said in a report: "The evidence suggests the actions of Pc McEwan, as the driver, were reasonable and what would have been expected of a police officer.
"He has explained the reasoning for both his actions and decision making, which appear to be in line with expectations."
The IPCC has ruled that there was no indication any officer involved had behaved in a manner which would justify disciplinary proceedings being brought.
Merseyside Police has agreed with the same findings and no further action will be taken against any officer.
Catherine Bates, IPCC operations manager, added: "I would like to offer our deepest sympathies to the family of Violet-Grace, who tragically lost her life in this terrible incident.
"We would also like to thank the police officers involved for co-operating with our investigation.
McAteer was later jailed for nine years and four months at Liverpool Crown Court after admitting to charges of causing death by dangerous driving and causing serious injury by dangerous driving.