Terence Wheelock, 20, died last Friday, three months after he tried to hang himself in a Dublin city centre station.
The Wheelock family, from Summerhill in Dublin’s north inner city, claim Terence sustained injuries while in custody and are demanding an independent inquiry.
The young man went into a coma after he tried to hang himself in a cell in Store Street Station on June 2.
Labour Party justice spokesman Joe Costello said an independent investigation was required.
“There are questions to be answered regarding how and why this young man, who according to everyone was happy-go-lucky, was taken into custody at one point and later ends up in intensive care.”
He said this was all the more so given Store Street Station had recently been refurbished amid efforts to make the cells suicide-proof.
Gardaí explained to the family that Mr Wheelock was found lying against a wall with a ligature - believed to be the cord from his tracksuit - tied around his neck. The ligature had been secured to a wall fixture.
Gardaí removed the ligature and gave mouth-to-mouth resuscitation and CPR. Mr Wheelock was taken to the Mater Hospital and put on a life-support machine.
Garda Commissioner Noel Conroy appointed Detective Superintendent Oliver Hanley of Dun Laoghaire to examine the case. The Wheelock family criticised this decision saying that the officer had spent a considerable period in Store Street.
“The commissioner set up an inquiry headed by a superintendent who served 15 years in Store Street.
“We still have not seen any light of the results of that,” Mr Costello said.
Mr Costello said that while he did not have any reason to believe there was any foul play involved in Mr Wheelock’s death, the family did have concerns.
“In the interests of everyone, gardaí and the family, we need to have an inquiry that is beyond reproach.”
A garda spokesman questioned media reports that there was extensive bruising on Mr Wheelock’s body.
The spokesman said that pending the outcome of Supt Hanley’s investigation it would be unwise to comment further.