Victoria University has raised questions as to how Baldwins - and the recruitment company which put him forward for the role - did not properly vet his credentials.
"Qualifications awarded by a university are a matter of public record and employers should check this as part of an appointment process," said Professor Penny Boumelha, deputy vice-chancellor.
"The university in-house solicitor will be writing to Mr Vukcevic today reminding him that all graduates must accurately represent their qualifications. At this stage, we are not planning to make a complaint to the police."
Cook Executive Recruitment handled the applications for the role at Baldwins but director Tim Cook declined to discuss what checks were made on Mr Vukcevic and referred the Herald to Baldwins.
Phone calls to Baldwins chairwoman Sue Ironside for comment were redirected to Piet de Jong, who works for PR firm Baldwin Boyle.
"Michael Vukcevic resigned from his employment at Baldwins for personal reasons in November last year. And the company has nothing further to add on the matter. That's our position," said Mr de Jong.
Mr Vukcevic, who has worked closely with government ministers and agencies negotiating free trade agreements in the Middle East, released a statement yesterday confirming he does not hold a law degree "from any university in New Zealand and have never worked in a legal role".
He said he didn't seek to mislead Baldwins, his appointment didn't involve legal work and he'd never been held out as a lawyer in any website profile. The statement does not explain how or why his CV states he obtained the law degree.
Michelle Boag, executive adviser to the Middle East Business Council of which Mr Vukcevic is the chairman, said the revelations yesterday were a "storm in a tea cup".
Mr Vukcevic had never claimed to have a law degree when dealing with the council, she said.
"As I understand it, he should have had the word 'incomplete' next to LLB. Having said that, I don't know why it wasn't there," she told RadioLive. "This is a voluntary board, people are nominated and elected. Like all council members, he's a volunteer, he receives no benefits from the work that he does."
Michael Vukcevic's full statement
I resigned from Baldwins on 15 November 2013 for personal reasons.
I do not hold a Bachelor of Laws from any university in New Zealand and have never worked in a legal role.
I did complete some papers towards a law degree at Victoria University but never completed the degree. I completed a Bachelor of Arts.
I did not seek to mislead Baldwins in my CV for the role. My appointment as chief executive officer of Baldwins did not involve legal work and Baldwins did not hold
me out as a qualified lawyer or patent attorney on their website.
Equally, I have never been held out as a lawyer in any website profile with the Middle East Business Council, any previous roles or on my LinkedIn profile or any business card.
I will not be making any further comment on my private employment matters.