It happened at a house in the Ballymacross Hill area of Lisburn yesterday, Sunday, 14 January.
Police say that sometime between 6.00am and 6.45am the front door of a house was set alight.
Scorch damage was caused to the front door and a wall.
There was also graffiti on the side wall of the house.
The occupants of the house, a man and a woman, were not injured as a result of this incident, however they were left very badly shaken.
Detective Constable Kenny said: “I would particularly like to thank the member of public who alerted the residents of the house.
“I would appeal to them and anyone else who may have information about this incident to contact Detectives at Lisburn Criminal Investigation Branch on the non-emergency number 101, quoting reference 366 14/01/18.
“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.”