The PSNI has come under pressure over taking part in a St Patrick's Day parade behind a banner reading 'England Get Out Of Ireland'.
This was the only banner permitted to be carried at the spectacle in New York City, according to the 2014 guidelines.
Six PSNI officers – including a chief inspector – marched in the Big Apple yesterday along with personnel from An Garda Siochana in celebration of the Irish saint.
Ulster Unionist MLA Tom Elliott queried whether the PSNI was aware of the banner rule and, if so, why the force permitted its officers to attend.
TUV leader Jim Allister furiously called on Chief Constable Matt Baggott to offer an explanation.
And DUP Policing Board member Jonathan Craig said he would be concerned if it transpired the officers travelled to New York using taxpayers' money.
Mr Allister accused Mr Baggott of a slight on unionists. He furiously rebuked the Chief Constable for the move and slated the parade as a "deliberately anti-British event".
"Why is the PSNI, a police service from the UK, officially participating in a parade behind an anti-British and offensive banner endorsing the 'Brits Out' message which saw the IRA murder so many gallant police officers?" he queried.
"Parading behind such a banner is no place for the PSNI.
"I am therefore demanding that the Chief Constable explain himself and this calculated slight on the unionist majority in Northern Ireland."
A spokesman for the PSNI told the Belfast Telegraph last night that it did not intend to respond to Mr Allister.
He referred the inquiry to a previous statement made by Assistant Chief Constable Alistair Finlay.
"We are delighted to have six officers in New York representing the PSNI and participating in the St Patrick's Day Parade," Mr Finlay said.
But SDLP leader Alasdair McDonnell – who attended the parade in New York City yesterday and marched along with the PSNI and Garda officers – spoke of his pride at the show of "brotherhood" between the two police forces.
"I am very proud to march alongside the brave men and women of both the PSNI and An Garda Siochana in New York," he said.
"It is important that, as the world celebrates St Patrick, Ireland and Irish identity, that we demonstrate how far we have come as an island and a people in breaking down the political and cultural differences that once bitterly divided us."
Mr McDonnell said it was important internationally for Ireland to show how far it had come.
"This is a gesture of the spirit of brotherhood between members of the PSNI and Garda in the face of shameful threat," he said.