A former Liberal staffer has resigned after accusations of sexist behaviour.

Tasmanian Greens leader Cassy O'Connor used parliamentary privilege this week to describe Liberal staffer Andrew Hudgson as a “sexist pig”.

Mr Hudgson has worked as a media adviser to federal Assistant Treasurer and Housing Minister Michael Sukkar. He also worked for former Victorian Liberal premier Denis Napthine and federal Cabinet minister Michaelia Cash when she was employment minister and minister for women.

He was asked to resign from his current role after Ms O'Connor made her statement.

She told Parliament a “personal story to tell about a vile insult Mr Hudgson directed at me” that her media adviser Alice Giblin heard during a media interview on February 1, 2019.

“Mr Hudgson called me a ‘meth-head c***’ as he and his colleagues walked across the lawns not far from us,” she told the Tasmanian Parliament on Wednesday night.

“Imagine hating women so much you'd say that audibly about a woman you don't know, who also happens to be an elected representative?

“I was doing an interview at the time and didn't hear the insult but Alice did. I believed her without question because in the decade I've worked with Alice she has never lied to me.

“Others who were with Mr Hudgson at the time heard it too. We know this. We've had it confirmed.

“Alice made detailed notes of her recollections, then reported this incident to the then-premier's office.”

Former premier Will Hodgman’s then-chief of staff, Tim Baker, received a complaint from Ms O'Connor that day, triggering a formal investigation by the Department of Premier and Cabinet.

After two weeks, Mr Hodgman said no further action would be taken.

“With respect to the specific allegation that Mr Hudgson yelled out and directed profanities towards you, the investigator has found the allegation to be 'not substantiated' and that Mr Hudgson did not yell out or direct profanities towards you,” the premier told the Greens leader in a letter.

“In making this finding, the investigator considered evidence provided by all interviewees including that:

“All witnesses, who were walking with Mr Hudgson at the time, stated that he did not yell out or direct profanities towards Ms O'Connor; and that as complainant Ms Giblin was unable to provide specific detail to further substantiate the allegation.

“Now that an independent and appropriate investigation has been conducted and concluded, I advise that it is my intention to take no further action in relation to your allegation.”

Ms O'Connor now says Mr Hudgson was “protected by the Liberal Party, state and federal”.

“And so, here we are. Andrew Hudgson's story was believed. He went on to work for the Morrison government.

“It reminds me a bit of the Catholic Church of old — shuffle people around, but keep them on the books.

“Madam Speaker, this is the standard our current Prime Minister walks past because, it becomes more clear by the day, he accepts it.

“The women and girls of Australia have long memories, Mr Morrison. We see you, we hear you, and we believe you are a big part of the problem.”