Gardai are investigating after "hate mail" was sent to the family of George Nkencho.
The 27-year-old was gunned down outside his home in Clonee, on the Dublin-Meath border, last Wednesday.
It has been widely reported that the letter contains racist and offensive language.
A garda spokesman said: "An Garda Síochána is investigating the origination and contents of correspondence which has been brought to our attention."
It comes as Mr Nkencho's family are set to meet with the Garda watchdog on Wednesday to question why he was shot dead by armed gardai.
The family, along with its Solicitor Phelim O’Neill, is demanding answers from GSOC about the circumstances of George’s death.
Mr O’Neill said: “It’s been difficult for the family and the wider African community
“There is an obvious desire to question why George was shot by armed gardai and have their questions answered.
“I have been engaged by the family to vigilantly scrutinise all the independent statutory processes that necessarily follow a tragedy of this kind, so we intend to actively engage with GSOC with a view to establishing the truth.”
The armed gardai who shot George said they responded to reports of a man wielding a knife at a nearby Eurospar supermarket and post office in Hartstown, where a shop worker is believed to have suffered a broken nose. The Nkencho family wishes to challenge unfounded claims about his character that have circulated online.
Statements made over social media have claimed that George, who was mentally ill, had multiple convictions and had only recently moved to Ireland from Nigeria.
Mr O’Neill told RTE’s Radio One: “It’s true that George certainly struggled with his mental health in recent years but he was a person of good character.
“The statements online that he only came to Ireland as a teenager in recent years are untrue.
“George actually grew up in Ireland, he lived peacefully with his family in Blanchardstown for over 18 years.
“The statements that he had a criminal record are untrue because George had no previous convictions.”
