The PSNI has recieved a report of gunshots being fired through the back window of a house in Omagh on Thursday night.
The incident happened at about 9.30pm, but the seven adults in the McClay Park house in the east of the town were uninjured.
The PSNI said on Friday morning that all lines of enquiry were being followed, and called for witnesses to come forward.
It is understood that those in the house were not foreign nationals.
The area is “100 per cent unionist” said independent councillor Patrick McGowan MBE.
He added: “They’d be very, very good people living there. I’d be surprised if there’s anything sectarian about it”.
Sinn Fein MLA Declan McAleer condemned what he said must have been a “frightening experience”, adding: “This is a community moving forward and we do not want this type of activity trying to drag us back to the past.”