A police investigation into an Irish tricolour flown from the roof of Parliament Buildings is still ongoing.
Almost two months after the rogue display, a PSNI statement said their inquiries - understood to involve seven detectives at one point - are continuing.
The Assembly Commission, which has suspended its own study of the June 3 incident, has said it can make no more comment until police enquiries are complete.
But a PSNI spokesman said there was also no indication when the police probe - into whether the display amounted to a criminal offence - would be finished.
Two flags, including an Irish Proclamation flag, were removed from the the roof where repairs were being carried out 13 minutes after they were first spotted, but not before the public had formally complained to the police.
Assembly director of facilities Stephen Welch said a number of security measures have been put in place to ensure a similar incident could not take place again.
And he said proposals were being prepared on the wider security arrangements and the "balance of risk" to Parliament Buildings.
An Assembly statement said: "The PSNI have begun an investigation into the circumstances surrounding this incident and whether they constitute a criminal offence. That investigation is ongoing and the Assembly is co-operating fully with it.
"The Assembly will make no further comment on this incident until the police investigation has been completed."
The SDLP's John Dallat said it was "laughable and lamentable" that seven detectives and three other officers appeared to be involved in the investigation.
"With serious crime on the increase, hundreds of murders unsolved across the North and harsh public sector cuts being implemented on the PSNI, having seven detectives tied up investigating a flag is scandalous," he said.
"Too much is being done to placate the calls of some people who simply have no sense of humour."
But TUV leader Jim Allister hit back: "This is the same Mr Dallat who, just a few years ago, complained bitterly about Translink flying the Union flag on designated days - which was perfectly legal. Now he complains that the PSNI are investigating a legitimate complaint about the improper display of foreign flags on Stormont."
A PSNI statement said: "We do not comment on operational matters, however where police receive a complaint we have a duty to investigate."