A video circulating on social media shows a group of men congregating around a lampost with traffic driving past, reportedly on Saturday night in the town.
One of the men then climbs on to the shoulders of the others and reaches up before pulling the Union Flag down.
The TUV says that the flag was one of many erected in the town for the recent visit of Prince Charles and the Duchess of Cornwall to the town - and that the removal and subsequent glorifying of the event on social media has angered local unionists.
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“The removal of a Union Flag over the weekend in Cookstown is yet another calculated effort by Republicans to raise tensions in the area,” said TUV Mid Ulster candidate Glenn Moore.
“Coming as it does so soon after the attack on Dungannon War Memorial this latest poke in the eye is irresponsible and insulting.
“Loyalists have shown remarkable restraint to date. There is an onus on the PSNI to do all they can to bring those responsible for both incidents to justice. Not only would this ensure the guilty parties were held accountable but it would go a long way to dispel the justified perception in Unionism of a two tiered police service.”
Sinn Fein and the SDLP were invited to comment.
The incident comes after wreaths were removed from Dungannon War Memorial in the early hours of Saturday.
Chairman of Dungannon/Moy Royal British Legion, David Cuddy, said: “At about 1am on Saturday morning all the wreaths were removed from Dungannon war memorial and scattered far and wide around Market Square.
“It was reported to the police who gathered up the wreaths again. Most of the 35 wreaths were ripped and damaged beyond repair.”
He called for the PSNI to make an appeal for witnesses.
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