Sheku Bayoh died in May 2015 while being held by up to 6 officers who were responding to a call in Kirkcaldy, Fife.
The 31-year-old’s family claimed race played a part in his death and they criticised the subsequent investigation.
Two officers involved in the death of a black man in custody may have provided false statements to investigators, A BBC Panorama investigation now alleges.
The officers had claimed father-of-two Mr Bayoh carried out a stamping attack on a female police constable before being brought to the ground and restrained by up to six officers.
However, a witness to the 2015 incident has told BBC Panorama the stamping attack “didn’t happen” and was not true.
Kevin Nelson was in a nearby house, and saw events unfold over a garden hedge.
Mr Nelson told BBC Panorama he saw Mr Bayoh attempt to walk away from the officers, ignoring their commands, before being sprayed with CS spray.
He said Mr Bayoh retaliated and punched PC Nicole Short but then ran off from where she went down and was quickly intercepted by other officers.
Asked if there had been any further contact with PC Short, he said: “No. He was running off… after the punch, there was no more attack on her at all.”
He added: “I didn’t see him stamping at all or, other than the punch, any raised arms. After the punch, that was it. There was no more attack on her at all.”
Both officers claimed that the stamping attack happened violently against the female victim with one officer saying “I thought he had killed her.”
The BBC said Mr Nelson’s account is supported by CCTV footage of the incident, obtained by Panorama which is poor quality but appears to show that once
PC Short is knocked down by Mr Bayoh, the action appears to move away from her, and Mr Bayoh is brought down within five seconds.
The Scottish Police Federation told the BBC that its officers had cooperated ‘truthfully’ with investigators.
A full public enquiry is currently underway.