More than 15 families have handed their files on the retention of the organs of their children who died in hospital to the Garda, according to the campaigning group Parents for Justice.
They want the Garda to investigate whether an offence was committed under the Coroners Act, which obliges hospitals to notify the coroner in certain circumstances where there has been a death in hospital.
Parents for Justice has been campaigning for a statutory inquiry into how and why the organs of their children who died in hospital were retained and disposed of without their knowledge or consent.
A private inquiry, under the chairmanship of Ms Anne Dunne SC, has been working on the issue since April 2000, but has no firm date for reporting, and Parents for Justice recently withdrew its support for this.
Parents for Justice has said it is aware of a number of instances where notification of children's deaths in hospital did not take place.
In a statement yesterday, it said that it fully supported families who decided to hand over files for the purpose of criminal investigation, although it was not encouraging people to do so.
The spokeswoman for the group, Ms Fionnnuala O'Reilly, said: "The families involved in this scandal have put their faith in the inquiry process established by the Minister for Health in February. Unfortunately, that inquiry has not had any degree of credibility for some time now.
"As a result, the Parents for Justice group withdrew from this inquiry, which was clearly unable to get to the truth of what we firmly believe to be criminal acts. The criminal acts I refer to are failure to notify the coroner of death in hospital where there is a statutory obligation on the hospital to do so."
The group is also seeking a meeting with the Minister for Justice to brief him on the situation, and especially on what the parents consider to be the issues under criminal law.
Section 18 of the Coroners Act lists the circumstances in which deaths must be notified to the coroner, including deaths under anaesthetic or within 24 hours of an anaesthetic. A person who fails to give such notification "shall be guilty of an offence" and liable to a fine of up to £20 on summary conviction.