The application, lodged with the Department of Primary Industries, Parks, Water and Environment by Lyons Labor MHA Jen Butler, requested a list of all exemptions including the name of the employer, the role performed by the employee, the date the application was received and the date the application was approved.

It was refused on the grounds the work involved would substantially and unreasonably divert resources from other work or it would interfere with the Minister's other functions.

In a letter rejecting the application, a RTI officer said the resources available to deal with the request were two FTE staff whose time was currently being utilised across 14 existing requests.

"In order to generate the information request, it is necessary to read an estimated 5000 applications. If a reading time of two minutes per application is allowed, it would take 167 hours, or seven full working days, just to read applications," the officer said.

"Requested information would need to be manually extracted from each relevant application and collated in a form that addresses the RTI request."

The officer said because personal information was contained in the exemption applications this would require consultation with affected third party individuals.

"An estimate of time to write to each affected business and individuals, say 2000 letters written, at 10 minutes per letter would require approximately 330 hours of staff time, or nearly 10 weeks," the officer said.

Ms Butler said the failure to release this information proved there was a veil of secrecy over the granting of exemptions.

"It stinks of a cover up," Ms Butler said.

"It is in the public interest to understand whether or not this process is a secure process.

"All we need is one mistake and that could be catastrophic for the people of Tasmania."

Communications, Electrical and Plumbing Union organiser Chris Clark said the fact the department could not fulfill the request raised serious questions over if its risk management plan was fit for purpose.

"This type of information should be readily available to potentially contact trace anyone who may test positive," Mr Clark said.

"We are led to believe many workers from Victoria have arrived in the state as recently as last week - it does not make sense that we don't have stronger risk controls in place."

When asked if it was in the public interest to release this information, Government Minister Roger Jaensch said because RTI requests were assessed at arm's length from the government he could not comment on the matter.