The Minister for Justice has been asked whether An Garda Síochána has ever provided information to the Central Statistics Office that contained the personal details of crime victims.
Labour TD Alan Kelly also asked whether the CSO has been given information about the "potential suspects" of these crimes.
Mr Kelly asked Minister Charlie Flanagan whether his department, or if the current or former garda commissioners were aware of it.
The Tipperary TD also queried whether the Statistics Act and/or the Data Protection Act had been breached.
"I want to know, the citizens of this State, their information, whether they were perpetrators of crime, victims of crime or indeed suspects ... that their information was sacrosanct and protected at all times," Mr Kelly said.
The minister said that if Mr Kelly had any evidence of wrongdoing he should put it in writing.
Mr Flanagan said that if there were any "irregularities" he would ensure an investigation took place.
The publication of crime statistics resumed earlier this year after it was suspended in June 2017 due to concerns over the accuracy of information provided by gardaí.