"Of course, we are concerned for her - she's 13," Detective Senior Sergeant Dave Greig said. "We are anxious to find out where she is."
Sarah is a Year 10 student at Hastings Girls' High School.
Principal Geraldine Travers said on police advice she had spoken to Sarah's form class about her disappearance.
"We have been co-operating with the police who have asked us whether any of the students had had any communication with her and might know her whereabouts," Ms Travers said.
"So I asked the girls to come forward if they could help because it is important that she is found, but as far as I know no one had any contact with her."
Messages from friends and family were mounting up on Sarah's Facebook page.
"I miss u my sissy. Come home please. Mum is fallin apart, Abby and I r freaking out. Stop doing this to us, please just come home or at least text me please Sarah," Sinclyre Winiata said on Tuesday.
"You wouldn't want your friends fretting over you. Let someone know you're safe at least. Hope you're okay xoxoxo," Sarah-Rose Jones wrote.
A message, including a photo and description of the teen, was also being posted online in the hope someone might come forward with information.
A friend of Ms Hodgetts, Cathy Brake, also wrote on Facebook this week claiming the 39-year-old mother had disappeared on the same day as the teenager.
"Leeanna has been missing since Tuesday 22nd May. She has not made contact with anyone - her two children and family are starting to get highly stressed," Ms Brake said.
Ms Hodgetts is European, regularly wears darkened prescription glasses and a beanie, has short hair, is short and of thickset build.
Sarah is described as Maori, about 1.6m tall and of medium build. She wears her hair long at the back, with a short fringe, and was last seen in a white hooded sweatshirt, brown woollen jersey and grey track pants.
The pair have connections to the Bay of Plenty, where there has been a possible sighting reported, and Auckland, and may be travelling in a dark blue Toyota Corona sedan, registration YK3034.
"I would urge both Leeanna and Sarah to go into their closest police station or at least make contact with their families, so the ongoing worry and stress caused by their disappearance can be alleviated," Detective Sergeant Craig Vining said.
Anyone with information about their whereabouts should contact their local police station or the Hastings Police Child Protection Team on (06) 873 0500.