Riot officers and fire and rescue teams were scrambled to Lorne Street, Leith, after reports of an intruder on the roof of St Paul’s Church earlier this year.
The Evening News understands that the suspect had been dressed as Batman and was planning to unveil a New Fathers 4 Justice banner at the church.
A source said the man had planned the protest after having problems winning custody of his child, who is believed to attend nearby a nearby primary school.
It is understood that he fled the scene when he heard the sirens. Police have so far not been able to track him down.
The drama unfolded at St Paul’s church shortly after 6am on February 12, when a concerned member of the public raised the alarm.
Officers cordoned off the area before more than ten riot police armed with shields searched the building.
The incident was scaled down just before 11am, when it emerged that the man had evaded police.
Officers insisted the large-scale response was “appropriate” due to the height of the building and the dense population of the area.
A spokesman said the number of officers was justifiable “given the dynamic situation”.
New Fathers 4 Justice, a national group which campaigns for the rights of fathers to see their children, declined to comment.
Its members often dress in superhero costumes.
In July 2008, two men in Spider-Man and Batman outfits climbed on to the roof of then-Labour Party deputy leader Harriet Harman’s house and draped a banner that read “Stop The War On Dads”. That came just a month after Ms Harman was first targeted by the campaign group as two men in superhero-style costumes and calling themselves “Captain Conception” and “Cash Gordon” scaled her house.
They said they would only come down if the minister agreed to read a book one of them had written, called Family Court Hell.
Other incidents have included a man staging a hunger strike outside Prime Minister David Cameron’s house in 2011 and another being jailed for six months for defacing a portrait of the Queen.
A Police Scotland spokesman said that no-one had been traced or arrested in connection with the Leith incident, but urged anyone with information to contact officers to help progress the investigation. The response echoed an incident in October, when riot teams and a helicopter were called to Cockburn Street to trace two men suspected of stealing a motorbike.
St Paul’s has not operated as a church for some time, and it is understood it has been used to store furniture in recent years.