A 29-year-old woman and her seven-year-old daughter escaped injury when four shots were fired into the living-room of their home at Bond Street in the Waterside area of Derry just before midnight yesterday.
Detectives investigating the incident said they were treating it as attempted murder and added that they believed a loyalist paramilitary organisation was responsible.
The woman and her daughter moved into the house from Belfast six weeks ago. The police said it was "too early" to speculate on whether the gun attack was linked to the loyalist paramilitary feud.
The police believe the shots were fired from a revolver and that the gunman opened fire on the house from an alleyway across the street. It is also thought the attacker escaped in a waiting car which was heard being driven from the scene at high speed immediately after the shooting.