Davidson added a hashtag to the social media posts - #DrivingWhileBrown.
"My bro is privileged enough to have the tools to respond politely to ongoing, systemic racism. The burden falls on him to be proven innocent. For others of our people, they can't live up to this burden…if we had armed cops, who knows…"
Davidson told the Herald there was ongoing research into racial profiling, and police themselves recognised the issue of "unconscious bias".
"It is ongoing and it is deeply rooted. And it is quite challenging to address."
Davidson said a way to change that was through projects like working with trainees at the Police College to discuss human rights and discrimination issues. However, a much wider effort was needed across all Government departments and agencies.
"There has been some positive signs. But it is probably going to take at least a generation of sustained work at all levels to stamp out and have a zero tolerance towards racial bias and profiling."
On her comment about not arming the police, Davidson said not everyone on the receiving end of racial profiling would behave calmly or politely, and that risked escalation.
"If we were to add into that equation guns, as we have seen in the States…it is people of colour and people on lower incomes who will be harmed in that interaction. We are fortunate we are not in that situation yet."
Davidson made the comments after linking to a Radio NZ story about Vuyiswa Tulelo, the South African High Commissioner to New Zealand, who said she was followed by a security guard every time she went to Countdown.
Davidson is not the only political party leader to speak out against racial profiling. When in Parliament Māori Party co-leader Marama Fox spoke of racial discrimination her son had suffered at school.
Fox has also spoken about how her daughters are regularly followed when they enter shops.
In February the Herald on Sunday revealed a young man caught with cocaine had escaped charges after an unprecedented exploration of racial bias by the country's second-highest court.
The man's legal team had argued police had no basis to approach the man's tidy, registered and warranted vehicle, and had only done so because its occupants were Pacific New Zealanders.
Although charges were later dismissed, the Court of Appeal didn't rule on whether racial profiling occurred. However, its judgment was the first to explicitly recognise racial profiling may take place among police, and well beyond.
"There is ample research which shows that unconscious bias exists, though [for those not negatively affected] it is rarely obvious and easily overlooked," the court stated. "Few who discriminate on the basis of race will admit it. Some will prefer to hide it. Most will be unaware of it and so will find the suggestion they do so insulting."
In response to the case, police strongly rejected the racial profiling allegation, but said training to combat "unconscious bias" was being stepped up.
Police Commissioner Mike Bush in 2015 said Māori over-representation in offender statistics could be partly explained by unconscious bias among officers.
