The Police Ombudsman is investigating how the PSNI enforced the coronavirus public health regulations at large public gatherings.
The PSNI faced claims of operating double standards earlier this week in dealing with separate rallies across Northern Ireland.
Up to 70 people were penalised for breaches of coronavirus regulations at anti-racism protests in Londonderry and Belfast on June 6.
However, a week later, there was not a single fine issued for a gathering to "protect" Belfast's cenotaph.
Several hundred people stood outside City Hall following an appeal from a group calling itself the Northern Ireland Cenotaph Protection Group (NICPG). It has called for war memorials to be protected amid attacks on statues of historical figures across Britain.
Many participants wore masks but social distancing guidelines were reportedly not followed by everyone at the event.
Assistant Chief Constable Barbara Gray said that the force had been faced with a "very different environment" from those at the Black Lives Matter protests.
A Policing Board member accused the PSNI of inconsistency.
The Police Ombudsman has opened its investigation after complaints from those that attended the Black Lives Matter protest at Belfast's Custom House Square and Derry's Guildhall Square.
The DUP called on the the investigation to be widened to cover all large gathering including "republican funerals".
The investigation is examining whether police were consistent in their approach to issuing fixed penalty notices.
Police Ombudsman Marie Anderson has informed the Chief Constable, Department of Justice and the Policing Board that she was beginning the work.
Mrs Anderson said her office received complaints about the enforcement of the health regulations at the Black Lives Matter protests when compared to other large gatherings such as those seen at beaches and at the “protect our statues" protest outside Belfast City Hall on Saturday, June 13 and concerns that police had not done enough to enforce the regulations.
She said her investigation will focus on the police policy and how it was and is being implemented, including how it is being communicated to police officers "on the ground".
Following the the Covid-19 outbreak, the Department of Health introduced health protection regulations, which included measures to restrict the movement of people from their homes and the numbers of people who could gather together.
The draconian measures received wide-spread support.
However, police were criticised over their handling of new powers to enforce the lockdown with some arguing they acted beyond what the legislation allowed.
The PSNI said it recognised the impact its actions in response had on public confidence but it had the backing of the Department of Health.
Assistant Chief Constable Alan Todd said the new laws could have been clearer. He also issued guidance for officers to seek approval from a superior before issuing fines for breaches.
The Police Ombudsman’s Office is empowered to investigate police policy and practice when it believes it is in the public interest to do so.
The legality of fixed penalty notices, however, is not a matter for the watchdog but rather one for the courts.
“The powers to enforce the public health regulations came under new legislation and there is the likelihood that they will continue to be enforced for many months to come," said Marie Anderson.
"It is in the public interest that there be an independent assessment as to whether the associated police policy is being applied consistently.
"If we identify inconsistencies and can make recommendations which will help improve policing of public gatherings, we will do so promptly.
"If, however, we identify that there have been good reasons for taking different approaches on occasions, that is something the public should know and understand,” she said.
The Policing Policing Board Chair Doug Garrett said he had met with the Ombudsman to discuss the terms of the investigation.
"This PONI investigation along with the review currently being progressed by the board’s Human Rights Advisor are both important for confidence in our policing service and evidence the robustness of the oversight arrangements in place here," he said.
"To avoid duplication, we have agreed there will be liaison between our respective offices in taking these forward.”
Following the gathering around the City Hall cenotaph at the weekend, ACC Gray added: ""To be consistent across such a range of issues we maintained our approach of engaging, explaining and encouraging.
"Enforcement will be considered following the substantial evidence gathering operation that was in place to record any potential offending."
She added: "While no fines or community resolution notices were issued at the City Hall, all evidence gathered will be reviewed to detect offences and we will work with our partners in the Public Prosecution Service to bring offenders to justice."