The police have been urged to spell out what kind of decisions senior officers can take without consulting board members.
Liberal Democrat justice spokeswoman Alison McInnes said clarity was needed because the term operational responsibility was frequently used to “stifle debate” on issues like the carrying of pistols to routine incidents.
Vic Emery, chairman of the Scottish Police Authority (SPA), has admitted he was not consulted before the decision was made which meant the body did not carry out any risk assessment of the policy.
The carrying of handguns has proved particularly controversial in Inverness and the Highlands where levels of violent crime have traditionally been low.
Highland Council deputy leader David Alston said: “Since the SPA is the body set up by parliament to exercise scrutiny on behalf of parliament and the public, this is a shocking bypass of democracy.”
Mrs McInnes, a north-east MSP, raised the issue with Derek Penman, HM Inspector of Constabulary in Scotland at Holyrood earlier this week.
Mrs McInnes said: “Surely it is not sufficient for the chief constable to assert something is his operational responsibility.
“It would be helpful to have a memorandum of understanding or a code that sets out some of the parameters.”
Mr Penman said the concept of independence was based on case law and convention.
“Operational independence still requires operational accountability and there is still the need for that accountability to take place,” he added.
“Although there are definitely decisions that are operational which means free from political interference, there is still the need for the chief constable to be accountable for these decisions in the framework that exists.”
Mrs McInnes claimed Chief Constable Sir Stephen House and Justice Secretary Kenny MacAskill have too readily dismissed legitimate questions and stifled legitimate debate with the “cry of operational independence”.
“There is no statutory definition of operational independence and what is becoming clearer by the week is that those two little words are being used to stifle legitimate debate,” she said.
Mr Emery has said the SPA “must do some work” to establish what operational decisions it needs to be involved in.
Two independent bodies are conducting reviews into the armed policing policy.