Curtis pleaded not guilty to all eight charges when he was arraigned at the Rotorua District Court this morning.
Judge Phillip Cooper said there had been "a huge amount of public concern and sympathy surrounding the circumstances of Nia's murder" and warned people called for jury service to speak to him if they thought they could not serve impartially on the jury.
He said this trial involved "quite separate allegations" to the trial of Curtis' sons, Wiremu and Michael, and the jury would be required to put aside feelings of prejudice and act in a "cool, calm, dispassionate and objective way".
Prosecutor Amanda Gordon also told jurors it was important that Curtis received a fair trial.
She said the case concerned events earlier in time than Nia's murder and that the jury needed to put out of their mind anything they had read or heard about the case.
The abuse Curtis is accused of relates to when Nia was living in a flat in James Street, Rotorua, with her mother, Lisa Kuka, and William Curtis' son Wiremu.
Also living at the flat was William Curtis' daughter, Hoana, who is set to be a key witness in the trial. Hoana was 16 at the time the alleged abuse between March 1 and July 1 last year.
Ms Gordon said Hoana would tell the jury about things she saw her father doing to Nia.
Hoana would describe seeing her father pick Nia up and throwing her, or slamming her, into the ground. She would allege that whenever he walked past Nia would push her and she would fall into the wall of the room she was in, Ms Gordon said.
She said Hoana would say that Nia would cry a lot and that William Curtis said: "F*** up if you don't stop crying I'll stomp on your head."
Hoana would also allege that William Curtis hit Nia across the face and made her mouth bleed but that the worst abuse she saw her father inflict on Nia involved him using a scarf.
"He picked up a black woollen scarf and he wrapped it several times around her neck, he then used the ends of the scarf to lift Nia Glassie off the ground to the point where she was hanging above the ground with her feet not touching anything," Ms Gordon said.
Hoana had said Nia was off the ground for about 10 seconds and just hung there until William Curtis left the scarf go and she fell to the floor. She then started to scream and he allegedly told her to "f*** up" again.
Ms Gordon told the court Hoana got so angry and upset when she saw William Curtis do that that she threatened to stab him.
Hoana told officers that several days after she'd spoken to police as part of their wider investigation she got a phone message from her father saying that she was a "snitch and that she was a little bitch and he was coming up there to slit her throat".
The "up there" referred to Auckland where Hoana was living at the time.
The Crown plans to call five other witnesses, including four police officers.
Curtis is represented by Harry Edward.
