Prosecutors have instructed the police to launch a formal investigation into allegations that pro-Union campaigners breached electoral secrecy laws during the referendum.

The development comes a week after police launched an initial assessment of complaints surrounding comments made by Scottish Conservative leader Ruth Davidson that postal vote "tallies" were being taken in the weeks before the referendum ballot closed at 10pm on September 18.

It has been confirmed that police made initial telephone contact with Ms Davidson yesterday, although party sources said there was "no suggestion she was accused of doing anything wrong at this stage".

On televised coverage of the referendum results, 45 minutes after the polls closed, Ms Davidson said that the No camp had been "incredibly encouraged" by the results of a "sample opening" of the postal ballot that she said had taken place around the country over the few weeks prior to the poll.

Complaints over her account of the postal vote "tallies" raised concerns the information may have helped inform the No campaign's decision to issue the "vow" of more powers for Scotland from the three main party leaders.

The Electoral Commission decided to pass complaints it received to the police after making an initial assessment over whether there was any case to answer. The independent elections watchdog decided it could be dealt with only by the police.

According to Elections Scotland guidance, referendum and postal ballot agents present at the opening of postal votes "must observe the requirement of secrecy".

Failure to observe the rules is a criminal offence, and is punishable by up to a year in prison and/or a fine of up to £5,000.

Yesterday, a Crown Office spokesman said: "We can confirm that Crown counsel has instructed Police Scotland to commence an investigation into alleged breaches of Schedule 7, Paragraph 7, of the Scottish Independence Referendum Act 2013."

Video footage of Ms Davidson talking about the ballot viewing was forwarded to both the police and the Electoral Commission.

In televised coverage she says: "Postal votes are going to be enormously important in this campaign; about 18 per cent of the vote is going to come out of postal ballots and we have had people at every sample opening, around the country, over the last few weeks, while that's been coming in. And we've been incredibly encouraged by the results."

Later, referring to postal ballots, she said: "Different local authorities have had openings around the country", adding, "there's people in the room that have been sampling those ballot boxes that have been opened and have been taking tallies and the reports have been very positive for us".

Political agents and campaigners are allowed to oversee the postal vote opening sessions, where checks are made to verify the signatures and dates of birth on postal voting statements against computerised records.

However, Elections Scotland instructions on postal votes state that it is "an offence for anyone attending the opening of postal votes to attempt to ascertain how any vote has been cast or to communicate any such information obtained".

On Tuesday it emerged that the Electoral Commission was looking to change the code of conduct for political campaigners in order to prevent them from handling any completed postal votes.