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Windows would be sealed up in the proposed repairs, because replacing them is too costly.
Patients were at risk of surgery delays when the building leaked, a staff report to members says.
Wet corridors in an already cramped theatre suite was another concern.
Repairs worth about $78,000 were already under way.
Board members, once the public are excluded from the meeting, would consider the request for ''up to $1.75 million''.
Last month, board chairman Joe Butterfield advised the bill for repairing leaks would be at least $1 million.
The building was nearing the end of its economic life; the repairs would allow its use for up to a decade, the report for tomorrow's meeting said.
Exterior windows could not be fixed, and would be sealed from the outside.
''The clinical services building exterior windows are constructed of a special aluminium extrusion which was manufactured especially for the clinical services building project in the 1950s.
''These windows are beyond their usable life and there are no parts or retrofits available.''
Replacing them was too expensive, given the expected lifespan of the building.
It was believed that most, if not all, of the windows could be sealed.
Air conditioning meant there was little need to open them anyway.
''There remains some risk of leaks with [this option] and the option of a hybrid solution with some full replacement will be made available to the contractors once closer inspection is possible.''
Scaffolding the entire face of the building would be required.
Scaffolding and window sealing would go out to tender, but staff are seeking permission to bypass a competitive tender to award the roofing contract.
The favoured supplier was a specialised roofing contractor with an excellent reputation, the report said.
''This contractor has undertaken an extensive ... survey on the roof and has identified a number of remedial items. The methods chosen and solutions proposed have been reviewed by [the building and property service] as the most cost-effective and efficient solutions.
''For other contractors to provide estimates, there would be further investigations required which would be time-consuming for both the contractor and [the board].''
An external quantity surveyor would be engaged to monitor and verify all of the costs associated with the project.
Contacted late yesterday afternoon, Health Minister Tony Ryall's office said it would not be able to respond to questions until today.
Last month, the Otago Daily Times asked Mr Ryall if the financially stressed health board would receive extra funding to cover the expense.
Mr Ryall's spokeswoman referred the ODT to the health board.