The prime minister called the posts "unacceptable".
Crime Scene Cleaners initially told RNZ families could not tell if their relatives' remains were in the photos and the posts raised awareness of problems like the country's suicide rates.
But the business later apologised.
The Office of the Chief Coroner has now confirmed staff spent just three days looking at the posts last month, before escalating the matter.
"Crime Scene Cleaners is being investigated by police on behalf of the Office of the Chief Coroner to confirm any breaches of the Coroners Act."
The investigation is a relief for victims' advocate Ruth Money who called for police to immediately investigate the company.
"Their behaviour was absolutely abhorrent, it certainly caused trauma for people."
She said there was "absolutely no reason" for the posts to go on social media, and she hoped the investigation would be "a stark reminder" for all companies trusted with sensitive information.
One woman - who paid Crime Scene Cleaners for a clean and later found photos of it on social media - told RNZ she hoped the police probe would force the business to "shut down".
She was "astounded" by the harm the posts caused her and others.
"I'm not sure if I believe in karma, but it definitely feels like a bit like they're getting what they deserve really."
She said staff from the company were lovely to her but not the owners.
"I actually ended up needing to go to my doctor for anxiety medication in order to help me sleep during that time and I was dealing with them. It was probably, so far, the worst time of my life."
The maximum penalty for breaching coronial non-publication orders is a $20,000 fine.
In a statement, Crime Scene Cleaners co-owner and general manager Carl Loader reiterated his company had "issued an apology at the time and are still deeply upset that our social media pages caused the reaction they did".
He said he had spoken to police and would "fully cooperate".
Meanwhile, Acting Privacy Commissioner Liz MacPherson is calling for people to come forward if they think Crime Scene Cleaners breached their privacy.
MacPherson told RNZ her office was collecting evidence.
"If we are not satisfied that the company is meeting its obligations under the Privacy Act, we have the ability to take enforcement action ... We're also managing a complaint from the public."
The enforcement can be anything from a warning letter, to prosecution and a fine of up to $10,000.
*To contact the commissioner's office call 0800 803 909 or email enquiries@privacy.org.nz
