SINN Féin is to seek a face-to-face meeting with the Chief Constable Matt Baggott.
It comes after the party’s North Belfast MLA Caral Ni Chuilin was taken to hospital following an incident involving a PSNI jeep on Friday night.
The incident happened after republican youths tried to provoke loyalists by breaking though lines of marchers during the Orange Order’s ‘Tour of the North’ parade in Belfast.
The PSNI has now referred the matter to the Police Ombudsman who has appointed a senior official to investigate.
The Sinn Fein Culture Minister was taken to hospital with ligament damage but has since been discharged.
It is understood the party want urgent talks with Chief Constable Matt Baggott and his senior commanders to explain the conduct of PSNI officers on Friday night towards two of its elected representatives.
Police said a 20-year-old man and a 16-year-old boy were detained for disorderly behaviour and provocative conduct following Friday’s Tour of the North parade, which also included suspected breaches of a Parades Commission determination.
Around 1,000 Orangemen and 15 loyalist bands took part in the annual event from 7pm.
The bands played hymns past St Patrick’s Catholic Church on Donegall Street and a small number of residents took part in a coinciding protest.
Bands are understood to have continued playing music, instead of a single drumbeat, while passing through the mainly nationalist area of Carrick Hill.
Police say a small number of nationalist youths also attempted to run through the bands as they made their way up Peter’s Hill.
There was a heavy police presence in the area and the atmosphere was described as “tense”.
A stand-off ensued, lasting about 15 minutes, after police in riot gear sealed off the area to keep rival groups apart.
Local Sinn Féin MLA Gerry Kelly said he and Ms Ní Chuilín also “moved quickly to restore calm to the area” before they were involved in the incident in which the Stormont culture minister was injured.
Mr Kelly hit out at police for what he called their “dangerous, reckless and provocative” actions.
“This is no way to deal with anyone, let alone elected representatives seeking to restore calm to an area in an already tense situation.”
Kelly said he approached the PSNI jeeps in which the 16-year-old boy was being held and asked to talk to the senior officer “on behalf of his parents”.
“We were told that this would happen if we moved aside. We did so yet the landrovers sped off”, he said.
Mr Kelly said he then stopped the third PSNI landrover and “demanded to speak to someone in charge”.
“The driver moved the landrover into me forcing me to hold on to a security grille on the vehicle when they drove off at speed taking me with them for a considerable distance.
“The group of people who had gathered tried to stop the jeep for my safety and Carál Ní Chuilín was injured in the process and has since been taken to hospital.”
The incident has prompted local DUP politicians to hit out at Sinn Fein’s Gerry Kelly.
Shankill Road DUP councillor Brian Kingston said: “Who does Gerry Kelly think he is trying to over rule the PSNI in their operational duty.
“It comes as no surprise that republicans cause trouble when an Orange parade passes off peacefully,” he added.
In a statement, the PSNI said: “The incident involving Gerry Kelly and Carál Ní Chuilín at Peter’s Hill tonight has been referred to the Police Ombudsman and they are investigating.”
Earlier Chief Superintendent George Clarke, District Commander for North and West Belfast said:
“Tonight’s parade was largely peaceful; however, there were a number of incidents, which are being investigated by police.
“These include suspected breaches of the Parades Commission determination and an attempt by a number of youths to disrupt the procession as it passed Peter’s Hill.
“Officers in the area of Peter’s Hill quickly brought the situation under control and separated the youths from the procession.”
The area has become a volatile flashpoint after a band was filmed playing a song perceived to be sectarian outside St Patrick’s Church on the Twelfth of July last year.
On Friday night a spokesman for the County Grand Orange Lodge of Belfast said the bands had shown respect to the Catholic church.
“This evening’s parade proved that the comprehensive template, issued earlier this month, was a genuine effort aimed at resolving the issue concerning St Patrick’s.
“Orangemen, women and bands paraded with dignity and showed respect at St Patrick’s Roman Catholic Chapel.
“We are saddened that citizens of this city of Belfast were prevented from walking along a main thoroughfare and it makes a mockery of a so-called shared city.
“We are glad the annual event passed off peacefully; we thank our supporters and look forward to celebrating our culture and heritage in a traditional manner.”
North Belfast DUP MLA Nelson McCausland commended all those who organised and participated in the Tour of the North.
“This was an excellent start to the main parading season, in spite of the spoiling actions of the Parades Commission,” he added.
But Frank Dempsey, from Carrick Hill Concerned Residents, expressed anger at the evening’s events.
“We told politicians this was going to happen. We told the police this was going to happen. Nobody did anything about it,” he said.
“This community is disgusted with the Parades Commission for the fact that they’ve issued two more determinations for parades to allow Orangemen to come down there playing hymns.”
Earlier, the Chief Constable Matt Baggott joined with NI political leaders to urge the communities to work towards ensuring that the summer marching season passes off peacefully.