West Midlands Police launched an investigation after the child and a family were using a pedestrian crossing when a car carried out a dangerous overtaking manoeuvre.
The vehicle overtook another car which was waiting for the pedestrians to cross Green Lane, in Castle Bromwich, Birmingham.
Footage of the incident, which happened at about 6.30pm on Monday, May 4 , has been circulating on social media.
This morning West Midlands Police revealed a man had handed himself into a police station on Friday night and had been voluntarily interviewed.
Officers said the investigation continues.
Sergeant Jon Butler, from the force's road harm prevention team, said: "We’re really grateful to members of the public who have submitted footage, and other information to us.
"We appreciate there has been lots of discussion about this incident online, and I want to reassure people that we are taking it seriously and are fully investigating in the way that the public would rightly expect of us."
Anyone with further information is asked to call 101. Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org
#UPDATE following near miss on pedestrian crossing in Green Lane, Castle Bromwich, on Monday 4 May: A 20-year-old man has been voluntarily interviewed after handing himself into a police station last night. Our investigation continues. pic.twitter.com/gv71ACTpBe— West Midlands Police (@WMPolice) May 16, 2020