Just 48 per cent of people north of the border believe the corporation does well at this - the lowest proportion of any of the countries in the UK.
The figure, which compares to a total of 58 per cent in England, was revealed in the BBC’s annual report,.
The report was released at the same time as the BBC revealed that presenter James Naughtie, from Radio 4’s flagship Today programme, will take on a key role in the coverage of the independence referendum.
The BBC has already announced a £5 million investment package to boost its coverage of the independence referendum, to be held in September 2014.
Naughtie, who has anchored several Radio 4 election specials and who covered the inauguration of the Pope for the station, will now host BBC Radio Scotland’s Good Morning Scotland programme two days a week.
The Scottish broadcaster will be back presenting on the Today programme full-time before the next UK general election in 2015.
Naughtie said he was “thrilled” about his new role in the run-up to the referendum.
“The constitutional debate and the decision next year have great historic importance for Scotland and the whole of the UK, so I am excited to be in the thick of it, on both sides of the border, from start to finish,” he added.
“The opportunity to spend more time working in Scotland in referendum year is something that I am looking forward to immensely.
“This is one of the great stories of our time and I’m delighted to be so involved in it.”
BBC Scotland director Ken MacQuarrie said: “The referendum story is of huge significance for BBC Scotland and I’m delighted James will be contributing to our coverage of it as part of the Good Morning Scotland presenting team.”
But the BBC Audience Council - which advises the BBC Trust on the views, needs and interests of audiences - said the corporation should be “more searching” in comparing differences in policy in the different parts of the UK in the wake of devolution.
It said: “Alongside the constitutional debate, the growth of increasingly distinctive public policy debates in Scotland calls for more differentiated journalistic treatment of these topics for audiences here.
“The council believes the BBC should be more accurate in reporting how the UK is governed, more searching in comparing public policy in the different nations and should achieve a better balance in reporting Scottish and non-Scottish news for audiences in Scotland.”
While the council welcomed the rise in programmes made in Scotland for the BBC network, it said its members were “disappointed that the increase has not led to more programmes reflective in some way of Scotland”.
BBC Trustee for Scotland Bill Matthews said: “This has been a difficult year for the BBC following last autumn’s revelations about Jimmy Savile, but I am pleased to see that BBC Scotland has performed well for audiences and there has been some outstanding content across a range of genres, with our Audience Council noting that there has been a step change in the quality and range of TV for audiences in Scotland.
“Our Audience Council has identified some areas that need further work. They have stressed the need to address the ongoing issue of finding the right balance of Scottish news and news which only affects other parts of the UK, and have highlighted that the network television programming made in Scotland should be more reflective of Scotland.
“Next year BBC Scotland will deliver comprehensive coverage of the Commonwealth Games and the independence referendum, bringing every development to audiences and making the most of the BBC’s online and digital capabilities.”