The institute fears that the percentage may rise to 50% from the currently proposed 35%. The move would force treasurers to expose to competition the more strategic finance functions like corporate accountancy and internal audit.
'This would strike at the very heart of the finance profession,' said head of CIPFA's competition advisory service Jeremy Kite. 'It would also hit at the core control function for finance,' he said.
'Finance is an increasingly scarce resource and so anything which jeopardises the quality and continuity of advice has to be bad.'
The rule applies to other corporate services facing competition.
Although the position was first laid out in a statement on support service costs at the end of last year, council officers are only now aware of its full impact.
'If the competition percentage of finance remained unchanged, not much work will have to be exposed to competition,' said Mr Kite.
He predicted the government would therefore move to tighten competition for finance departments forcing councils to expose strategic services to CCT.
'We believe the DoE is currently revisiting the percentage for finance,' he said. 'Our expectation is it could go to 50%.'
Most treasurers are currently considering satisfying the percentage requirement for CCT by exposing revenue and payroll services. Both have a large IT element.
Mr Kite urged the DoE to stick with the current proposed percentage, saying many of the aims of CCT, such as rationalisation of management structures, had to be achieved because of financial constraints placed on councils.
A final announcement on the percentage is expected before the end of May.
Finance services in metropolitan councils and London boroughs - along with most other core council services - are due to be exposed to private competition for the first time from next year. Shire councils will have CCT for these white-collar services delayed until after they are reorganised.