Whether they were in a relationship at the time of the death is unclear.
It is understood a hammer was found at the scene by police.
Schofield spoke to police at the station, before being charged with Ms Drummond's murder.
The 49-year-old appeared calm and attentive in the dock at Rotorua District Court yesterday morning, clad in a white boiler suit and wearing glasses.
The names of Schofield and Ms Drummond were initially suppressed by Judge Phillip Cooper, but the accused murderer was brought back before the court about 3.30pm when suppression was lifted.
Schofield was remanded in custody to reappear on May 13.
His lawyer, Andy Schulze, said Schofield had "no difficulty" with what Judge Cooper was suggesting when suppression was ended.
Ms Drummond's death was not the first tragedy to hit the family.
She and Schofield are the parents of Zara Schofield, who was violently attacked in 2008 by Jahche Broughton less than a fortnight before Broughton murdered Scottish tourist Karen Aim in Taupo.
Ms Drummond's workmates at Millennium Hotel and Resort, where she worked as a cleaner, were left shocked after news of her death emerged yesterday.
"It's a very big shock to all of us here and I have some very, very upset staff," general manager Diane Kerins said.
The staff had "nothing but respect for her", she said.
"We're all devastated, actually.
"It's very sad that this should happen to such a sweet, happy, joyful person to work with.
"She didn't have a mean bone in her body. We only saw kindness from her."
Yesterday, the house was cordoned off and under guard as forensics investigators carried out a scene examination.
Neighbours said they heard no sign of an altercation on Tuesday afternoon and were shocked to see police cars arrive at the street.
One neighbour, who asked not to be named, had known Ms Drummond since the pair sat together in English class at Tauhara College and described her as a "lovely lady".
The two often talked about their cats and Ms Drummond's three daughters, Zara, Lana and Casey.
"I saw her quite regularly as she'd be getting in the car to work, and we'd always say hi." Another neighbour who knew Ms Drummond said her thoughts were with the woman's three daughters.
"I just feel incredibly saddened by the situation and the impact that's going to follow, especially on her children but also extended family. They lose more than once."
The neighbour was at work on Tuesday evening but knew something was wrong when she came home to find police and an ambulance parked in the street, with security overnight. But it was not until she checked the news the next morning that she realised Ms Drummond was dead.
"I just felt sick in the guts, angry and distressed."
Police were due to finish the scene examination last night, before a post-mortem examination in Auckland today.
