However, Crown Law opposed prosecution.
"Almost ten years have now passed since the collapse of the CTV building...and still we have no justice, no accountability, and no closure," family spokesperson Maan Alkaisi told media in Christchurch today.
Alkaisi said there was overwhelming "compelling" evidence that should have been tested in the courts.
He told media the IPCA had responded to a complaint laid by families, which he claimed disputed the police and Crown Law decision not to prosecute.
They would not initially release the IPCA report, but sent it to media later on Monday afternoon.
The IPCA report said the decision of the police not to lay charges for manslaughter was an "appropriate exercise of their discretion and not unreasonable".
However, it did acknowledge it was inappropriate for the families to learn of the police decision not to prosecute only through the media.
Alkaisi said families were calling for the Prime Minister to independently review the decision-making process the police went through prior to deciding not to press charges.
"We respectfully request that the prime minister appoint one of two retired judges to independently review and report on the robustness and integrity of the decision-making process in respect of the Police decision not to pursue prosecution."
He asked for CTV families to be included in the drafting of the terms of reference and scope of a review.
"We maintain that the CTV case must go to trial to ensure justice. A court of law is the best place to test the strength of the case," he said.
"We feel that we have been let down at all levels."
Wellington lawyer, Gary Turkington, was providing legal advice to the families and said there were multiple avenues available to them, which included appealing to the United Nations.
In response to the families' concerns raised today, a police spokesperson said the organisation conducted a four-year investigation to determine the potential criminal culpability of individuals in connection with the deaths of 115 people following the collapse of the CTV building during the 22 February 2011 earthquake.
"The outcome of the investigation was that there would be no criminal prosecution in relation to the collapse of the building due to the fact that the evidence available was not deemed sufficient to provide a reasonable prospect of conviction in court."
The Prime Minister, Jacinda Ardern, said she would look at the letter sent to her by families today outlining their concerns.
She said she "totally" understood why the families had made the call for a review but wanted to look at the letter before responding.
