Four people were in the house in Princes St when shots were fired at the window and front door.
Residents of the area said gunfire was heard at around 1.40am this morning.
Residents said they were wakened by the sounds of gunfire and a car speeding off.
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A front window in the property is badly damaged as is the front door.
A PSNI spokesperson said: “Detectives are investigating a report of a shooting at a house in the Princes Street area of Lurgan in the early hours of this morning, Monday, 5 September.
“At approximately 2.00am a number of shots were fired at the house. Damage was caused to the front door and a living room window.
“There were four people in the house at the time of the incident. No one was injured, however the occupants were left very badly shaken.”
Detective Sergeant Colin Patterson would appeal to anyone who may has information about this incident or who witnessed any suspicious activity in the area to contact Detectives at Lurgan on the non-emergency number 101, quoting reference number 82 05/09/16. Alternatively, if someone would prefer to provide information without giving their details they can contact the independent charity Crimestoppers and speak to them anonymously on 0800 555 111.
Doug Beattie MC MLA said this afternoon: “I have spoken to PSNI in Lurgan who are currently dealing with the incident and are treating this as a hate crime. We must allow them time and space to investigate fully-anyone with any information I encourage to call 101.
“We cannot tolerate the use of firearms under any circumstances on the streets of Lurgan. This endangers all members of the community and must be condemned.”