"I have no recollection of receiving the same but I do not doubt I would have received it," Peters told lawyers for the Crown, according to a High Court judgement issued last week.
"I note the letters contents and given nothing had changed since I applied for National Superannuation, I doubt I would have given it anything but a cursory glance. I had no reason to think the details would be other than correct as there had been no change in my life relevant to the National Superannuation payment."
In an earlier answer, Peters said he had been living "with his partner of many years" when he signed his super application form in 2010.
The court heard Peters had argued "an error had been made when the form was completed".
"The plaintiff's analysis is that the MSD processed an incomplete form and made the mistake so that it was the MSD who made the calculations, not the plaintiff," the court said.
In an interview with the Herald, the Deputy Prime Minister this week said he had no intention of halting the case and that it would be going to court next month.
"51,000 people have made mistakes over the years on superannuation. One made the newspaper," he said.
"It's a matter of privacy. It's important in our society. Privacy is critical to the quality of life and what you might say is the majesty of life of being a New Zealander."
He declined to comment further because the case was before the courts.
In the court decision, Justice Geoffrey Venning has ordered Peters to expand on a number of answers to questions asked during preliminary stages of the case.
That includes, for example, clarifying whether he was living with his partner, Janet Trotman, in March 2014, whether he had contacted the Ministry of Social Development about the letter, and who he believed had told media about overpayments.
Peters' legal team have argued there "was no direct evidence of who was responsible for the leak" but the court ruled the question needed to be answered.
"If the answer is the plaintiff does not know, then that should be recorded," Venning said.
Peters' lawyers objected to the orders for more information in general;, saying he had given "all admissible evidence" he had.
Peters has also subpoenaed NewstalkZB political editor Barry Soper to give evidence in the case.
The defendants in the case include the Ministry of Social Development, Brendan Boyle, State Services Commissioner Peter Hughes, the Attorney-General on behalf of the Ministry of Social Development, Paula Bennett, the former National State Services Minister and former Minister of Social Development Anne Tolley.
About four weeks before the 2017 election, Peters revealed he had been overpaid the old-age pension for seven years, but that he had repaid the undisclosed amount as soon as he had found out.
He pro-actively revealed the overpayment in a press statement because media outlets had been asking questions about it.
National has consistently denied having leaked details.
