She is also seeking a waiver of application fees, as she says she is facing financial hardship.
"I am a widow since 2004, and I sold my only piece of land for the sake of my son's studies in New Zealand instead of Canada, as he thought this to be a more peaceful country," she wrote.
"After my husband's death, I started work in a religious organisation at a salary of just $100 per month."
The case will be returning to court on October 15, and Ms Kaur said she was keen to be in New Zealand to follow the proceedings.
Speaking through an interpreter, Ms Kaur told the Herald yesterday she was still struggling to get over the pain of losing her son.
"His death sent my whole world crushing down, because the family had placed our entire hope on him," she said.
"I have invested everything, including selling my ancestral land, to help him go to his dream country so that he would be able to get a good qualification and job, but it is all gone now."
Mr Singh had a diploma in IT and came to New Zealand to study, find a good job in the industry and settle.
He took the security jobs to help pay his bills while looking for other work.
Ms Kaur said she had another son, aged 24, in India.
He was a physiotherapy student, but was not as academically inclined as Mr Singh.
She will return to India tomorrow, but hopes to come back when the murder trial starts.
The New Lynn Sikh temple Gurudwara Sri Harkrishnan Sahib has been providing assistance for Ms Kaur during her stay in New Zealand, and a temple spokesman said members of the community will "support her 100 per cent" if she was granted residency.
"This is where her son promised her she will end up one day, and I think we owe it to him to make that promise come true," the spokesman said.
A spokeswoman for Mr Groser said yesterday the minister had not received Ms Kaur's letter.