Curtis (49) allegedly wrapped a scarf twice around the 3-year-old's neck, then lifted her off the ground and strangled her with it until she was purple.
The allegation was made by his daughter, who said he also slapped Nia's face, threatened to stomp on her head, and would walk up to the toddler and push her on to the ground or into the wall.
Curtis has denied the allegations, pleading not guilty to charges of assaulting and injuring Nia with intent to cause grievous bodily harm between March 1 and July 1 last year.
His trial will begin on Thursday in the Rotorua District Court and is expected to last two days.
His sons, Wiremu and Michael, were found guilty of Nia's murder on November 18.
The jury accepted the brothers kicked Nia in the head on July 20 last year, causing fatal head injuries.
The pair were also found guilty of wilful ill-treatment and a series of assaults on the little girl, including spinning her on a clothesline until she fell off and placing her in a tumble-drier.
Nia's mother, Lisa Kuka, was found guilty of manslaughter for failing to provide medical treatment for her daughter and failing to protect her from violence.
Two others, Oriwa Kemp and Michael Pearson, were convicted of wilful ill-treatment and assaults.
A sentencing date for the group is yet to be set.
