A woman and her six-year-old son escaped injury after a petrol bomb was thrown though the window of their Coleraine home.
The incident happened at a house on the Silverthorn Avenue in the Harpur's Hill area of the town at around midnight on Wednesday.
Police say the device did not ignite, leaving the woman and child uninjured.
Local Alliance councillor Barney Fitzpatrick has condemned those behind the incident.
"I am shocked and disgusted at this," Mr Fitzpatrick said.
"This must have been a horrific ordeal for the woman and her son. People in the town will be appalled at the incident.
"Those who are behind incidents like this must be caught. It is difficult to comprehend how anyone could be involved in something like this."
It is understood that a motive for the attack has not yet been established. Local detectives have appealed for information.
© UTV News