Davidson said Baron's resignation was covered by a mediated confidential settlement.
In a statement, Southern District commander Superintendent Paul Basham also refused to comment.
"The individual you have named is a former member of NZ Police," he said. "We do not discuss employment matters relating to current or former staff and have no comment to make."
An earlier information request from a member of the public about the matter was also turned down, for privacy reasons, and because police said making the information available would "prejudice the law".
Baron's 2015 appointment was a much-lauded event, with a press release at the time labelling it a "milestone" for the district, because Baron was the first woman to hold the job.
A Dunedin local, Baron had previously held a range of roles within police, including frontline policing, youth, prosecutions and leading case management across the district.
The road policing role was a very public one, with Baron regularly fronting appeals about speeding or weather, in a bid to improve safety on the roads.
"My vision is for our roads to be the safest in the country and our team will take a strong stance on unacceptable behaviour," Baron said in the June 2015 announcement.
"Road safety is the responsibility of everyone."
The then-Southern District commander, Superintendent Andrew Coster, said he was "delighted" to have Baron as part of the district leadership team, saying she was an "extremely competent leader and manager".
Police are yet to appoint a replacement manager for the road policing team.
