Tasmania Police will not investigate Health Minister Michael Ferguson over allegations he revealed the medical information of Angela Williamson to her employer, Cricket Australia, before she was sacked for tweeting about abortion.

Shadow Attorney-General Ella Haddad last week asked Tasmania Police to investigate Mr Ferguson, who is also Police Minister, over claims he had revealed medical information about Ms Williamson to Cricket Tasmania chief executive Nick Cummins.

The Opposition has also called for Premier Will Hodgman to launch a code of conduct investigation into Mr Ferguson over the claims.

Ms Williamson said she was sacked by Cricket Australia over tweets she sent from a private account that were critical of the Tasmanian Government's position on abortion.

Mr Cummins later rang Mr Ferguson to apologise over the tweets.

Ms Williamson has claimed that during the call Mr Ferguson disclosed details of her own termination to Mr Cummins, who was her boss at the time.

When referring the complaint to police last week, Ms Haddad said Mr Ferguson may have breached the Personal Information Protection Act.

The State Government has consistently denied any wrongdoing, and said Mr Ferguson had not disclosed any information that was not already on the public record.

A police spokeswoman said no investigation into Ms Haddad's complaint was warranted because the substance of the complaint did not constitute a criminal offence.

Mr Hodgman said the Labor Party should cease making "baseless claims" in relation to the matter following the police decision.

Ms Haddad said Labor would continue to demand an independent investigation.

Ms Williamson has taken Cricket Australia to the Fair Work Commission.

Labor and independent Murchison MLC Ruth Forrest have previously called for an independent investigation into the Government's involvement in the saga.