An investigation is going on in the theft of a Sangh flag, which was being flown in a Civil Service Bhawan in London to mark the birthday of Queen Camilla.
BBC News NI understands that an Irish tricolor was made in its place.
The departments of the communities said that it was known about the “unauthorized” removal of the union flag from its offices in Lisahli on 17 July.
The Northern Ireland Police Service said it was considered as “communal hatred crime”.
Under the law, every year the flag of the Sangh is flown from government buildings in Northern Ireland in nominated days.
On July 17, it was being flown by Civil Service Building in Lisahli to mark the 78th birthday of Queen Camilla.
The department did not confirm that the Irish flag was parked on flagpole.
But BBC News NI has spoken to workers who say that this was the case.
PSNI said that on Thursday afternoon, the theft of Union Flag was reported and he appealed to anyone to come forward for information.
The Democratic Unionist Party (DUP) described the removal of the union flag and its replacement with the Irish tricolor as a “foolish act”.
“Such foolish attention behavior is derogatory and completely unacceptable,” Fool MLA Gary Middleton said.
“Those involved in this should be dealt with by law.”
Ulster Unionist Councilor Darren Gai said that responsible people were fuel by “hatred and communalism”.
“In the last few weeks, we have done theft and barbarity works in the entire city and district,” he said.
“The sculptures of the constable nodded a memorial in Artigervan; a historic American flag stolen from Foyal College; Khasakhas wreath was to be removed soon after being kept in memory of Som’s battle – one left side was stolen that night and there were countless attacks on Protestant houses in the fountain. [a mainly unionist estate],
The cows criticized SDLP and Sin Fen in response to similar incidents.
“Nevertheless, these actions fueling with hate and sectarianism continue, unwanted, unwanted, to their own elected representatives.
“If this is now acceptable, it is not surprising that the Sanghists would never want to be a part of the pipe dream which is a joint Ireland.”
But the criticism was rejected by Sin Fen and SDLP.
Sin Fen said that it was “uneven, consistent and vocal”, stating that all cultures should be respected.
“All and every incident of hatred crime should be called out,” said a spokesman.
“In contrast, we have seen the selective approach and double standards of the unionist politicians in response to illegal bonfire and hatred crimes.”
SDLP MLA Marc H Durkan said that incidents are harming community relations.
“SDLP has always urged tolerance around these issues and condemned those who are engaged in any attack, communalism or intimidation,” he said.
“I would urge anyone involved in such activity to stay, they are not achieving anything other than hurting their city.”