An independent investigator has been appointed to look into allegations of bad behaviour by Liberal MP Sam Duluk at a parliamentary Christmas party.

Key points: The ABC has confirmed the investigator is Paul Hocking, of Quark & Associates

The ABC has confirmed the investigator is Paul Hocking, of Quark & Associates Mr Hocking has 24 years' experience as a licensed inquiry agent

Mr Hocking has 24 years' experience as a licensed inquiry agent The investigation is expected to be complete in four weeks

It is alleged Mr Duluk slapped SA Best politician Connie Bonaros on the backside at a parliamentary Christmas Party in December.

He issued an apology on Twitter following the claims, saying he was "deeply sorry for any actions that have caused offence".

The Member for Waite is also facing allegations he sent Ms Bonaros unwanted text messages, and that he made inappropriate remarks to two female staffers.

Mr Duluk has relinquished the chairmanship of Parliament's economic and finance committee and said he would seek professional help for his alcohol use.

However, Premier Steven Marshall has said he would await the results of an investigation before taking any further action against his MP.

The Opposition has criticised the probe taking place behind closed doors, saying there had been no guarantee the investigation would be released publicly.

In a statement, Liberal MP and Speaker Vincent Tarzia, said he had appointed an independent investigator with "considerable experience" undertaking confidential investigations dealing with complaints made within the public sector.

The ABC has confirmed the investigator appointed is Paul Hocking of Quark & Associates.

The company's website states Mr Hocking has 24 years' experience as a licensed inquiry agent, after working as a senior detective with the Northern Territory Police Force.

"The scope of the independent investigator's inquiries will be to endeavour to obtain full particulars as to what took place concerning the alleged conduct of Mr Duluk and to provide a report for the Speaker's consideration," Mr Tarzia said.

The four-week inquiry will be 'of a confidential nature'

Mr Tarzia said the inquiry would be "of a confidential nature" and is expected to be complete in four weeks.

It is not clear if the results of the investigation will be made public.

Greens MLC Tammy Franks requested he be removed from a parliamentary committee she sat on with him.

The Labor Opposition has called on the Premier to sack Mr Duluk, with Opposition Leader Peter Malinauskas labelling the allegations as "serious".

"These claims of inappropriate behaviour by Mr Duluk in Parliament House warrant a thorough, independent and transparent investigation," he said.

"How can South Australians have confidence in this investigation if it is shrouded in secrecy?

"Why has the Government refused to appoint the Equal Opportunity Commissioner or [another] appropriate government agency to conduct this inquiry?

"South Australians have a right to know the details of an investigation into Mr Duluk."