The Chief Minister, Treasury, and Economic Development Directorate has been paying the union to deliver work health and safety training and awareness to Canberra workplaces for the past 13 years, without going to competitive tender.

Originally, the funding, now worth about $121,000 a year, was tied specifically to a position within UnionsACT, described as a "work health and safety liaison officer".

But that position no longer exists, and has been changed into a policy and research role, which is now filled by former ACT Labor branch president, Australian Education Union industrial officer, and ministerial staffer, Garrett Purtill, who does have some work safety experience.

UnionsACT and the directorate both say that's because the funding arrangement changed in May, and is no longer tied to the "liaison officer" position.

The directorate said the purpose of the funding is to raise awareness of WHS issues in workplaces, facilitate access to training, provide support and advice on work safety, and undertake research.

UnionsACT was also disqualified as a registered training organisation by the Australian Skills Quality Authority in May, because the authority says it failed to pay its annual fees.

That is again dismissed as insignificant by the directorate and UnionsACT, who say the union does not need to be a registered training organisation to provide the service is it being payed for.

UnionsACT secretary Alex White also disputes ASQA's claim that the deregistration occurred due to a failure to pay fees, saying he voluntarily asked for the union to be taken off the register because it was unnecessary.

"We requested last year to be deregistered, and that is on the basis that we are not providing that training anymore," he said.

But the Canberra Liberals said the arrangement was questionable, and Deputy Opposition Leader Alistair Coe said he planned to refer it to the auditor-general.

"In the interests of transparency and given the record of the Barr government, the auditor-general should investigate this issue," he said.

But Mr White said the Liberals were obsessed by the issue, which has been the subject of two reviews and public debate in the Legislative Assembly.

"The obsession that Mr Hanson and Mr Coe have with this decade-old issue show they have no positive vision for working people in Canberra," he said.

Mr White said UnionsACT was not acting as a training provider, but rather facilitated and gave advice on WHS training.

The funding arrangement recently changed, following a review.

It is now paid out annually under a deed of grant, instead of the quarterly appropriations paid previously.

The directorate said the funding arrangement had been reviewed twice in the past to check whether UnionsACT was using the money appropriately, and would continue reviews annually.

The first review was conducted in 2011, and recommended that the funding be renewed, but subject to stricter reporting requirements.

"There are arrangements in place to review the use of the grant funds on an annual basis to ensure it meets its objectives," a spokeswoman said.

"The ACT Government has already conducted two reviews in the past, in 2012 and 2014 to ensure that UnionsACT achieves the grant's objectives and the ACT Government receives value for money."