Father of five Nazim Din, 54, suffered a cardiac arrest on Grasmere Court in Wortley on August 28, 2013.
It came after police arrested his eldest son, Nadeem, on suspicion of criminal damage.
Officers had also put his other son, Naveed, into a police van because of uncertainty over the brothers’ identities. Mr Din collapsed as he protested Naveed’s innocence.
On the fourth day of his inquest in Wakefield yesterday, neighbour Niaz Ahmed told the jury he had seen an officer – known to be PC Paul Richardson – push Mr Din before he fell.
Speaking through an interpreter, he said: “He said to police officers ‘Release my son’ and then the police officer pushed him with his arm and he fell down. When he was on the floor he (the police officer) just walked back a few steps.”
He later said he thought the push had happened as the officer tried to shut the doors to the van Naveed Din was in.
Under questioning, Mr Ahmed, who said he didn’t “trust” police, said he could not recall what sort of a push it was but added: “I swear on the Qu’ran what I said was true.”
Mr Ahmed said he did not speak to any neighbours that night about what happened.
But that claim was contradicted by other witnesses who gave evidence in court.
Maxine Coultas said Mr Ahmed initially told her police had “touched” Mr Din to try to guide him away from the van his son was in. She said he only later claimed he had seen the officer push him as rumours started to circulate.
She said: “I feel like the first conversation was what he had actually seen and the second one was what everybody else had told him.”
Her husband Philip Coultas also said Mr Ahmed only mentioned a push in a second conversation that night.
The inquest continues.