A mum and her two sons are alleged to have been forced from their South Belfast home by the UDA.
Alliance councillor Kate Nicholl said the woman felt she had to take action over fears for the safety of her children and their friends.
Police said they received a report of an assault in Benmore Drive, Finaghy on Sunday evening.
Kate said she has written to the PSNI about the incident.
"It is outrageous to hear how this family has been treated, in a community that is opening and welcoming to all," she added.
"I have raised this issue directly with the PSNI and am seeking further clarification as to what is being done to reassure the wider South Belfast community who will be very troubled by these depressing headlines.
"South Belfast does not belong to any one person, the only people not welcome in Finaghy are these criminals."
A spokesperson for the PSNI said enquiries are continuing.
They added: "Police received a report of an assault in the Benmore Drive area of Belfast on Sunday evening (September 6th).
"Officers were made aware of a possible link between this incident and an altercation occurring in the Benmore Drive area which is reported to have taken place on Friday evening, September 4th. Enquiries are continuing.
"A 40-year-old man was arrested on suspicion of assault and released pending a report to the Public Prosecution Service."
Whilst police do not discuss the security of individuals, should they receive information that a person's life is in danger it is understood they are informed accordingly.
