A post-mortem examination will be carried out on a baby boy who died in Waikato Hospital two days after his mother had died at the same hospital.

The newborn died on Wednesday night after being in critical condition since his birth on Monday.

His mother, Casey Missy Turama Nathan, 20, of Ngaruawahia, died at the hospital on Monday night after complications during childbirth.

She had given birth at a birthing unit at Huntly before being transferred to the hospital.

Both deaths had been referred to the Waikato coroner.

"Comments on the cause of death of either person at this time would be inappropriate and it is for the coroner to establish this in due course," Senior Sergeant Mike Underwood said.

Police have criticised some media for their coverage of the deaths, including two outlets which reported the baby had died when he was still alive.