The attack happened at Mourne View Park in Lisburn.
The PSNI say officers received a report that a number of petrol bombs had been thrown at a ground floor window of the flat at around 2.30 am.
The window was broken and scorch damage caused inside the flat as a result.
No-one was at home at the time of the incident and there were no reports of any injuries.
Three men were seen leaving the area on foot shortly after the incident, one wearing a light coloured hooded top and the two others wearing dark coloured hooded tops.
Detective Constable Chris Perks is investigating the incident and has appealed to anyone with any information which could assist the investigation to contact detectives in Lisburn on 101 quoting reference number 241 12/06/16.
Information can also be given anonymously through the independent charity Crimestoppers on 0800 555 111.