The incident occurred in the Parkmore area of Craigavon.
It is believed one bullet struck a window pane of the house and a further two struck a car that was parked at the property.
No one was injured during this incident.
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There were two people, a male and a female, in the property at the time.
Chief Inspector Jon Burrows said: “Did you see any suspicious persons or vehicles in the vicinity of Parkmore in the early hours of this morning? Do you have any information that could assist detectives with their enquiries? If so, please contact detectives at Lurgan on the non-emergency number 101, quoting reference 64 09/05/19.
"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.”