A Chinese martial arts instructor who abandoned his toddler on a Melbourne railway platform strangled his wife to death, the Auckland District Court was told this morning.

Naiyin Xue is accused of murdering Anan Liu, 27, between September 11 and 13 last year.

It is alleged that after he killed her in Auckland he fled with their three-year-old Qian Xun Xue - dubbed Pumpkin - and abandoned her on a Melbourne railway station platform.

Xue, 53, was arrested on the outskirts of Atlanta, Georgia, on February 28, after a six-month manhunt across the US.

Two Justices of the Peace began a two day deposition hearing this morning with high profile barrister Chris Comesky acting for Xue and Brian Dickey for the Crown.

Mr Dickey told the court that evidence will show that Mrs Liu died from ligature strangulation, carried out by Xue with a yellow coloured dress tie that he owned.

The death followed a sequence of domestic violence which saw Mrs Liu move away with the child to Wellington.

Mr Dickey said Xue went to Wellington with an axe to do harm to .... his wife.

The intention was to get her to return to Auckland.

The hearing will determine whether a case exists to send it to trial in the High Court.

Most of the evidence is to be submitted by consent and Mr Dickey said he would call six witnesses.

At the end of the expected two day hearing Xue will be asked to plea to the charge that he killed his wife.