Police have confirmed they had a presence in the area when a loyalist gang removed a poster belonging to hardline republican party Saroadh.
The sign is believed to have been taken from the Irish Street area of Dungannon at around 9.15pm last Wednesday.
Footage of the incident appears to show hooded loyalists with their faces covered taking the poster, which was attached to a roadside railing.
In one clip, a PSNI officer stands yards from the gang as they remove the sign.
The police officer can be heard saying "you are handling stolen goods" and "you are liable to arrest and prosecution".
Another clip shows a group of men running away from two police officers while carrying what appears to be the republican poster.
Another short film, which is believed to have been produced by loyalists and circulated on social media, gloats about the theft.
In the video it is claimed that "as the PSNI guarded the poster they (police) took video footage of those involved while threatening arrests".
"Back up was called and huge resources used for several hours to try and apprehend those responsible," the loyalist video claimed.
The video says "loyalists made their way across the town and removed this republican hate display".
A spokeswoman for the PSNI last night said: "An officer was in the area of Irish Street when the poster was removed and requested assistance from other officers in the area.
"Officers responded however the group had dispersed before their arrival.
The spokeswoman added that "a poster was removed from the area and taken by the men, who then made off along William Street and then towards Barrack Street."
