The family of a young man who died in similar circumstances two years ago have expressed their "heartfelt condolences" to Brunton's family.
Nicky Stevens, the son of Hamilton city councillor Dave Macpherson, stepped out for an unsupervised cigarette break while a patient at the Henry Bennett Centre.
His body was later found in the Waikato River.
Macpherson said the family wished to "express its great sorrow" to Brunton's family.
He said "one-size-fits-all" DHB policies that make mental health patients stand in the street to smoke were putting them at risk.
Waikato DHB did not accept responsibility for Stevens' death.