Seven people escaped injury when a number of shots were fired at a house in Omagh on New Year’s Day.
The shots were fired through the rear window of a house in McClay Park just before 9.30pm.
Police said the adults were left “badly shaken”. A spokesperson said all lines of inquiry were being followed.
Sinn Féin MLA Declan McAleer condemned those responsible: “This attack on a house at McClay Park is wrong and must be condemned.
“Thankfully no one was injured in this incident but it must have been a very frightening experience for those in the house and their neighbours.
“Those responsible for this incident do not represent the views of the community in Omagh.
“This is a community moving forward and we do not want this type of activity trying to drag us back to the past.
Mr McAleer added: ”I would urge anyone with information on this attack to bring it forward to the PSNI.”