Federal Opposition Leader Bill Shorten says a Tasmanian woman's sacking from Cricket Australia, allegedly over political opinions shared on social media, demonstrates the need for a national anti-corruption commission.

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Ms Williamson took to social media to criticise the Tasmanian Government's closure of abortion services, and was soon after sacked from her government relations role at Cricket Australia.

She has alleged a senior member of the State Government had disclosed to her employer the fact she had a pregnancy terminated.

Ms Williamson has lodged a complaint with the Fair Work Commission, fighting against what she claims is an unfair dismissal.

At times nearing tears, Ms Williamson said she believed her dismissal was unfair because her political opinion had nothing to do with her work.

"You can't terminate a position based on political opinion," she said.

"It's really clear that the political opinion I was expressing on my personal Twitter account had nothing to do with my job, and everything to do with my personal experience."

She said she felt the need to post her opinions on social media during the public debate over abortion services in Tasmania in January of this year, when the last private provider of the termination services closed, as she felt it important to restore the services in the state.

"There was a lot of trust in this process," she said.

Opposition Leader Bill Shorten said it was concerning there may have been an information leak from the Government's office.

"Women in Tasmania do not have access to the same medical resources that women on the mainland have," he said.

"This is wrong, and it just shows you the Liberal Party don't get health care.

"If they have released private health information, or if they have sought to have this woman blacklisted, that shows you why we would need a national anti-corruption commission."

Upper House member calls for inquiry

Documents showed the email account of senior Liberal staffer Martine Haley was used to send screenshots of Ms Williamson's tweets about abortion to Cricket Australia in an apparent attempt to have her reprimanded.

MLC member for Murchison Ruth Forrest also wants an inquiry into the Government's role in Ms Williamson's sacking.

Tasmanian Upper House independent Ruth Forrest wants an investigation into the State Government's role. ( ABC )

Health Minister Michael Ferguson has already said the Government was not responsible for decisions made by Cricket Australia.

Mr Ferguson said the Government had not discussed any private material "that wasn't already in the public domain" with Cricket Australia.

Ms Forrest described Ms Williamson as a "brave woman".

"It's just disgraceful that her reputation is being dragged through the mud over a personal experience she dared to share," she said.

"The Government's and Cricket Australia's actions continue the shaming and stigmatisation of women, regarding their sexual and reproductive health."

Premier Will Hodgman echoed Mr Ferguson's comments, saying nothing had been discussed between the Government and Cricket Tasmania or Cricket Australia that "wasn't on the public record".

"No one in my Government, me nor Minister Ferguson, have ever sought to influence the employment decisions of Cricket Tasmania or Cricket Australia in any way whatsoever," he said.

'Stressful debate' at a difficult time

Ms Williamson had to travel to Victoria for an abortion.

"I think when you're sharing your deepest thoughts, and how you feel, and how dark it can get, or how lonely or afraid — I'm an educated woman with the financial means to do what I did, and I just thought there were a lot of voices in Tasmania that didn't have that access," she said.

"I was also pregnant at that time, and I was making a decision about a termination right then and there.

"I'd be watching the news or looking at Twitter, and hearing federal and state ministers telling me what's available, and it was not what I was experiencing at all. I felt invisible.

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"There was no personal story or evidence to put colour or light or feelings to a really important issue and instead it was black and white writing, and language that was hard to swallow.

"It was really confronting to hear the language being used by the Government — they were using words like 'abortion on demand' and 'hospitals are there for saving lives', and this language just really didn't match with what was needed."

She said she believed the decision over her dismissal had a lot of input from both Cricket Tasmania and Cricket Australia.

"I believe that they felt that by me expressing my views, my political views and my experiences on this particular issue, that I'd compromised my relationship with Government," she said.

She claimed the social media policy cited as the reason for her dismissal did not say anything about her personal opinions.

"The social media policy allows you to talk about personal matters and issues. It's very much focused on if I were to say negative things about cricket or cricketers or colleagues," she said.

"So I felt that my surgical termination and my situation and political opinion had nothing to do with being able to look at who to invite to a cricket match, or how to collaborate on important cricket matters or issues."