Murdered An An Liu only married Nai Yin Xue so she could stay in New Zealand, a court has heard.

A friend of the couple, Xiaoxing Ding, told the High Court at Auckland today that Ms Liu told her during a telephone call that she married Xue so she could get residency in New Zealand.

Ms Ding said Xue told her that when she got residency Ms Liu refused to sleep in his bed and was cool towards him.

Xue is accused of murdering Ms Liu in September 2007 by strangling her and dumping her in the boot of his car. He then allegedly fled the country with his 3 year-old daughter, abandoning her in a Melbourne railway station.

Ms Ding also told the court Ms Liu had told her that their daughter slapped her father in the face, causing him to push the little girl away.

Ms Ding said she thought it was wrong for a child to do that but Ms Liu told her Xue had a problem controlling his temper.

Another witness earlier told the High Court that the pair's marriage was "cold" and Xue's attitude towards Ms Liu was "distant".

Graham McNamara, a former friend, did martial arts training with Xue for about six years and visited his house on several occasions.

Asked by Crown prosecutor Aaron Perkins to describe the relationship he said it was cold and there was "no warmth in the house".

Mr McNamara said Xue's attitude towards his wife was "stand-offish".

He told the court of a time Xue got upset with him after he gave Ms Liu a kiss on the cheek when he greeted her.

He said she looked upset but when he did it Xue, who he knew as "Michael", became angry and walked out of the room, saying something in Chinese.

On other occasions he went to see Xue he noticed an "imbalance" in their relationship. "Michael was in control," he said.

An example of the control he had over her was he would ask her to do things and if she or their daughter came into the room he would ask her to leave.

He stayed friends with Xue but fell out with him soon after Ms Liu left for China in 2004.

In cross examination, Mr McNamara admitted he didn't know much about Chinese culture and accepted that Chinese people were generally more reserved than New Zealanders.

The trial continues.