The Federal Opposition's 'smoking gun' theory about the investigation into suspended Labor MP Craig Thomson appears to have been shot down in Senate estimates.

Liberal Senator Eric Abetz demanded Fair Work Australia be called back to estimates last night after he was provided with a 2009 internal memo that mentioned the possibility of referring the investigation into the Health Services Union to police.

The memo was released after FWA had finished at the estimates hearing on Monday night, and the Opposition accused FWA of trying to bury it to avoid answering questions.

But in estimates last night one of the email's recipients told senators there was not enough evidence to refer the matter to police in 2009.

FWA's Ailsa Carruthers told Senator Abetz that the union "simply did not have sufficient evidence" at that time.

"We were not in a position to have identified any malfeasance," she said.

"In my view - and this is my view - we were a long way in June 2009 from being able to have any view as to whether there was potentially criminal behaviour in this matter."

The email was sent by Doug Williams, the former head of the Australian Industrial Relations Commission, the body which was replaced by Fair Work.

In it Mr Williams says there should be a clear plan and actions arising from the outcome of the inquiries to date, including referrals to other authorities like the police.

The email also went to the head of the HSU investigation Terry Nassios, who is now on leave from Fair Work Australia until the end of January next year.

The estimates committee was told that Mr Nassios might have appeared before the committee, but said he had not been asked.

An exchange with Mr Nassios will now have to wait until the next round of Senate estimates later in the year.