Victoria's deputy chief health officer did not breach the department's code of conduct when .
But she has since been spoken to about the potential for social media use to undermine community trust in the public service and has deleted Twitter from her work phone.
Deputy Chief Health Officer Annaliese van Diemen faced calls to resign last week, following her controversial tweet posted on the 250th anniversary of Captain James Cook's landing.
"Sudden arrival of an invader from another land, decimating populations, creating terror. Forces the population to make enormous sacrifices & completely change how they live in order to survive. COVID-19 or Cook 1770?" she tweeted.
Liberal backbencher James Newbury referred the tweet to the state's public service watchdog, who released its investigation into the matter on Tuesday.
It found Dr van Diemen did not breach the Department of Health's code of conduct in posting in the tweet.
Department of Health secretary Kym Peake said Dr van Diemen was spoken to about the risks of social media use when working in the public sector.
"The risks of private use of social media when working in the public sector, and in particular when occupying a role that involves high profile public communication, have been discussed with Dr van Diemen," said the letter from the Victorian Public Service Commission.
"In addition, Ms Peake has advised the commission that Dr van Diemen recognises the risk of diverting attention from the critical public health messages to the community and has subsequently removed her Twitter account from her phone."
In a statement, the Department of Health said it will not be taking any formal disciplinary action.
"The department supports Dr van Diemen and the incredible role she has played and will continue to play, in fighting this virus," a spokeswoman said.
The incident, however, has prompted a review of the department's social media guidelines.
Treasurer Tim Pallas said Dr van Diemen was doing an "exceptional job" in responding to the pandemic.
"I don't think that it's a matter worthy of any great comment or scrutiny and certainly not criticism from the government," he told reporters on Tuesday.
Mr Newbury said Dr van Diemen should apologise or delete the tweet.
"A real sign of remorse would be to delete it," he told 3AW.
"Victorians shouldn't be paying public servants to be left-wing political activists, it's really that easy."
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