James Hayward has pleaded not guilty to four charges relating to the alleged abuse of an eight-year-old girl.
The 52-year-old resigned from the WA Nationals after the charges were laid in December but has continued to sit in the upper house as an independent.
Hayward last month asked a Perth magistrate to vary his bail conditions so that he could travel to Queensland to attend a medical cannabis symposium.
He told the court via an affidavit that he would have to resign from a parliamentary committee investigating the regulation of medicinal cannabis if he was unable to attend the conference.
Prosecutors did not oppose the application for Hayward to leave the state for four days and it was granted by the magistrate.
The government's leader in the upper house Sue Ellery later told parliament there were no standing orders or conventions that enforced travel on any committee members.
"For a member of the Legislative Council to misrepresent to a court the practices and rules of the Legislative Council is a serious matter," she said.
"It has the potential to bring the council into ridicule or disrepute."
Legislative Council president Alanna Clohesy on Tuesday referred the matter to the powerful Procedure and Privileges committee, saying she was satisfied the alleged conduct was serious enough to warrant investigation.
The state Labor government has meanwhile faced criticism after the premier, deputy premier and two senior ministers were absent from parliament on Tuesday.
Premier Mark McGowan and Energy Minister Bill Johnston had travelled to Collie, 200km south of Perth, to announce the closure of coal-fired power stations by the end of the decade.
Deputy Premier Roger Cook and Emergency Services Minister Stephen Dawson were both overseas.
Opposition Leader Mia Davies labelled their absence arrogant, particularly while WA was still in a COVID-19 state of emergency.
"We've had pieces of legislation dropped in our laps as opposition at short notice, they've been rammed through using their numbers," she told Perth radio 6PR.
"We're only sitting 20 weeks this year. It's not a heavy sitting schedule. I just think it's contemptuous and disrespectful."
Parliament will sit for two weeks this month before a six-week winter adjournment.
Senior minister Rita Saffioti said the government had subjected itself to scrutiny despite its commanding majority in parliament, even lending the opposition two MPs so they could put through a motion condemning the government.
"I can tell members that that would never have happened under Colin Barnett or Richard Court," she told parliament.
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