In a debate about armed police Mrs Mitchell, the Conservatives’ justice spokeswoman, said the logic which suggested that people who carry knives are more likely to use them could also be applied to firearms.
Her comments come against a background of news accounts suggesting armed officers can in some cases atincidents where there is no suggestion of any need for weapons.
This is said to be because officers are despatched to incidents based on where they are and whether they are available to deploy.
Police are routinely armed on the continent, but in the UK the concept remains controversial.
She said: “The fact that hundreds of police officers are carrying firearms while responding to everyday duties is deeply disturbing for the public.
“These fears have been heightened by the unacceptable lack of transparency and accountability in decision making by Police Scotland on this issue in particular.”
She added: “It has been consistently acknowledged that someone who carries a knife is in danger of using that weapon or becoming a victim of knife crime.
“It’s an interesting analogy with the arming of police, because there is a real apprehension that if police officers routinely carry a weapon, that weapon will be used in a manner other than that intended.”