One of yesterday's positive Covid-19 cases is a woman who gave birth prematurely at Rotorua Hospital, and whose baby later died.

The woman and her partner both tested positive for Covid-19 after arriving at the hospital.

Lakes District District Health Board chief executive Nick Saville-Wood said they were a young couple going through a difficult time and there was not much more he could say for privacy reasons.

"Because the baby was born prematurely and our hospital doesn't look after that particular age group for those premature births, we transferred the baby up to Waikato Hospital," he said.

"The mother didn't go with the baby but we were talking to the mother this morning about potentially going up to see the baby."

He said the couple were from Auckland and were now isolating with a family member in Rotorua.

Meanwhile, 12 police staff in Rotorua are self-isolating and waiting for test results after coming into contact with the couple on Saturday afternoon.

Police would not provide more information for privacy reasons.

Two staff from Rotorua Hospital are also isolating and waiting for test results.