The attack happened at Alfred Street Place in Ballymena.
Detective Chief Inspector Dunny McCubbin said: “We believe that a petrol bomb was thrown at the property around 3.45am this morning.
“Three adults and a 12 year old boy who were in the house at the time were uninjured.
“A window in the house was smashed and scorch damage caused to an exterior wall.
“Anyone who saw anything suspicious in the early hours of the morning should contact detectives at Ballymena on the non-emergency police number 101, quoting reference 147 of 21/4/17.
“Alternatively, if you would prefer to provide information without giving your details, you can contact the independent charity Crimestoppers and speak to them anonymously on 0800 555 111.”