A spokesman for the Department for Business was quoted as saying a new version of the postal service would have to be created.
Labour's Shadow Postal Affairs Minister Ian Murray said: "End-to-end postal delivery is expensive and the SNP has to do more than just say everything will be the same. Alex Salmond has many questions to answer. What would be the cost of sending letters inside and outside of Scotland? How would the jobs and pensions of Royal Mail staff be secured? And what would happen in areas of rural Scotland that are currently supported by a guaranteed UK-wide service."
The Scottish Government said that after independence deliveries would continue uninterrupted.
A spokesman said: "The existing methods of delivery available to the people of Scotland when sending mail to other parts of the UK will continue.
"We do not anticipate any significant change from the current UK-wide system.
"The Scottish Government has a clear commitment to maintain a universal service obligation."
But Labour described the response as vague.
In comments reported at the weekend a Department for Business spokesman said: "In the event of a Yes vote, UK public organisations would remain with the rest of the UK. It would be up to an independent Scotland to create new ones."