Belfast City Council workers were flanked by police as they removed a banner which targeted Belfast's Lord Mayor John Finucane on Monday.
The banner contained allegations about the Sinn Féin North Belfast election candidate and his family.
It had been erected in the Tiger's Bay area of north Belfast.
Supt Melanie Jones said police were in attendance "to ensure the safety of persons removing a banner from council property".
"Enquiries are underway to establish if these banners constitute any criminal offence or offences, including a hate incident or hate crime," added Supt Jones.
Sinn Féin leader Mary Lou McDonald said there has been an "appalling and dangerous" campaign of "harassment, intimidation and threats against John Finucane and his family".
He is a candidate in next month's Westminster election in the North Belfast constituency, which is also being contested by outgoing DUP MP Nigel Dodds and Nuala McAllister of the Alliance Party.
Mr Finucane's father, Pat, was a solicitor who was shot dead by loyalists at his home in north Belfast in 1989.
The DUP said the party was "unaware" of the banners but said that if they have been reported to the police, then anyone with information should speak to the Police Service of Northern Ireland (PSNI).
A spokesperson added: "The DUP consistently condemns violence or anyone inciting hatred. Will Sinn Féin now condemn those behind the many Provisional IRA murders in North Belfast?"
'Hatred and division'
The PSNI said it has also received reports about banners erected in south Belfast and added enquiries are being made.
SDLP leader Colum Eastwood said there had been banners erected which targeted candidate Claire Hanna in south Belfast.
"The banners that have been erected in Belfast targeting John Finucane and Claire Hanna seeking to sow hatred and division are disgusting," said Mr Eastwood.
"Those responsible are cynically using, abusing and retraumatising victims for narrow political purposes."