PC Alannah Ramsay said she had been asked to speak to Iranian-born Ahdieh Yazdanparast in 2011 and took a statement.
The Stirling-based officer said the woman said had told her that her husband had threatened to pour acid on her face and he did not care if it affected their children.
Asked by advocate depute Tim Niven-Smith if she had also claimed that, in her words, "he would ruin my life", PC Ramsay said: "Yes."
Ahmad Yazdanparast, 61, has denied murdering his 46-year-old former wife on October 12 last year at the Venus Hair and Beauty Salon in Maxwell Place, in Stirling. It is alleged that he assaulted the hairdresser and poured petrol or a similar flammable substance on her head and body, ignited it and set fire to her and that she was so severely injured she died later that day in hospital.
It is also alleged Yazdanparast had evinced malice and ill-will towards her.
Yazdanparast, who ran a takeaway business, has lodged a special defence at his trial at the High Court in Edinburgh maintaining that he acted in self-defence.
The court heard from another police officer, PC David Collins, 33, who had spoken to the now deceased woman in 2012. She had given a statement in which she said her husband had been shouting and swearing at her in Iranian and that he was shouting he was going to kill her.
The court heard that the couple were divorced last year after protracted proceedings.
The trial continues.