The gun attack took place on a house in the Enniskeen area of Craigavon at approximately 1.10 am.
There was one male present in the house at the time of the incident. He did not sustain any injuries, however he was left badly shaken.
A short time later police received a report that an Insignia car had been burnt out in a laneway in the Eastway area of Lurgan.
Police believe this vehicle may have been involved in this incident.
Detective Inspector Stephen Harvey would appeal to anyone who saw any suspicious persons or the Insignia car in the area of Enniskeen or Eastway to contact Detectives, Criminal Investigation Branch, Lurgan on the non-emergency number 101, quoting reference 77 05/10/17.
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.