Shortly before midnight on Tuesday, 23 January, a petrol bomb was thrown through a bedroom window of the flat.
A female, who was in the bedroom at the time, sustained minor injuries from flying glass.
There was also scorch damage caused around the window and a bedroom door.
Detective Sergeant Peter Crothers would appeal to anyone who noticed any suspicious activity in the area or who has information about this incident to contact Detectives at Ballymena Criminal Investigation Branch on the non-emergency number 101, quoting reference 10 24/01/18.
Alternatively, information can also be provided to the independent charity Crimestoppers on 0800 555 111 which is 100% anonymous and gives people the power to speak up and stop crime.