A file is being prepared for the Public Prosecution Service on potential breaches of lockdown rules at a Republican funeral in County Tyrone, police have said.
Photographs on social media showed a large crowd at the funeral of Francie McNally on Wednesday.
Mr McNally was a former Sinn Féin councillor from Ballinderry.
Police said some mourners "blatantly ignored health advice", putting others "at risk."
Deputy First Minister Michelle O'Neill told the daily press conference at Stormont "no one is exempt" from the guidance on social distancing.
The PSNI said talks were held with Mr McNally's family and a local priest before the funeral to “stress the requirement for social distancing.”
'People put at risk'
Mid Ulster district commander Supt Mike Baird said: "The family had assured us only family members would be in attendance.
"It is very disappointing to see some people blatantly ignored health advice and breached current legislation by attending the funeral.
“In doing so, they not only put themselves at risk but also put at risk close family members of the deceased and those officiating at the funeral.”
Police said they are continuing to gather evidence.
Speaking to BBC News NI, Fr Peter Donnelly, parish priest of Ballinderry, said he was unaware of what happened before the remains of the late Mr McNally arrived at the church.
He said there was no church service because of the current Covid-19 guidance.
Fr Donnelly also stressed attendance at the committal service in the cemetery was limited to 10 immediate members of Mr McNally's family.
All current guidelines on funerals were strictly adhered to in the church grounds, he added.
First Minister Arlene Foster said it was right that the PSNI is investigating the case, while Chief Constable Simon Byrne said bereavement was not an excuse to behave in a selfish way.