The government at budget time announced it would need to find $450 million in savings across all departments to ensure the budget remained in surplus.

It has repeated promises there would be no cuts to any frontline services.

There was recently a switch between heads of departments where Health Department secretary Michael Pervan left his post to go to Communities Tasmania.

That department head, Ginna Webster, switched to the Justice Department and that department's secretary, Kathrine Morgan-Wicks, left to head the Health Department.

Ms Morgan-Wicks formerly worked with the Treasury Department.

In Question Time on Thursday, Mr Hodgman failed to answer whether DPAC and Treasury staff had been sent to the Health Department this week to identify where cuts could be made.

He denied Labor leader Rebecca White's assertion that Ambulance Tasmania had been requested to slash $5.7 million from its budget.

"We have not done and will not do what she suggests," Mr Hodgman said.

Ms White said the cut would be equivalent of the cost to keep 37 paramedics employed.

"We are already seeing stations being unable to open because they can't get enough paramedics to fill the roster," she said.

"This will have significant impact not just on the staff but on our communities."