The attack happened in the Thornlea area of Omagh.
Detective Inspector Trevor Stevenson said: “We received a report just after 8.15 pm that shots had been fired at a house in the area, striking the front door and window.
“A man and woman were inside at the time.
“While they were thankfully uninjured, both have been left badly shaken.
“A black motorcycle with two riders was seen leaving the area, heading towards Deverney Road.
“We are appealing to anyone with any information, or who may have seen this vehicle, to contact us on 101, quoting reference number 1801 of 13/08/19.
“Alternatively, information can 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.”