The Ramogibe family in Vosloorus on the East Rand claims Mdluli featured prominently in the last days of their son, Oupa Abel Ramogibe.
The family alleges that Mdluli and Oupa were both in love with a Vosloorus woman, known only as Tshidi, who had a child with Mdluli.
The family says Mdluli came to the Ramogibe family home looking for Oupa.
Oupa's mother, Sophia Ramogibe, told Sowetan that Mdluli took her to Oupa's siblings' homes and when they could not find him, Mdluli warned that if he found Oupa before the family brought him to the Vosloorus police station, "there will be mourning" in their family.
A few days later, Oupa was ambushed while driving a car belonging to another Vosloorus policeman, but survived the attempted hit.
Oupa reported the matter to the police.
According to Sophia Ramogibe, a policeman who introduced himself as Dlomo came to her house looking for Oupa. When he did not find him he asked her to tell him to come to the police station.
"I feel like I led my own son to his death. Had I not relayed that message, perhaps my son would still be alive today," she said.
After arriving at the police station Oupa was taken to the scene of his ambush.
"The police's own version is that Oupa was busy showing them what happened when someone came from nowhere, drew a gun from the holster of the investigating officer, shot and killed Oupa," said Oupa's brother Mohau.
"The man then ran to an awaiting Golf, dropped the gun and fled. The police did nothing when all these things were happening."
Vosloorus head of detectives Solly Phago said: "Mdluli has no case. He has never been investigated for any offence."
Phago said if the family has a case number they should come to the police and he would help them.
Yesterday Mdluli told Sowetan that he would not comment on the relationship between himself, Oupa and the woman, who has since died.