Policing Board member Ross Hussey called on anyone with information about those responsible to pass the information to the PSNI.
“Nothing, absolutely NOTHING, can justify such an attack anyone with any information should contact PSNI on the 101 non-emergency number,” said the MLA for Omagh.
Detectives have launched an investigation over the gun attack.
Police say seven adults escaped injury during the gun attack in Omagh, Co Tyrone.
Officer say a number of shots were fired through the rear window of a house in McClay Park just before 9.30 pm on New Year’s Day.
The adults were left “badly shaken”and were treated by paramedics at the scene for the effects of shock.
The family have lived in the home for the past year but it is not believed to racially motivated or sectarian.
Detectives are said to be checking out all lines of inquiry to find out who fired shots at the house and why.
Anyone with information can contact police in Omagh on 101.