Two petrol bombs were thrown during a incident at a house occupied by a man, woman and two young children in Dungannon last night.
One was thrown at the property in the Killymaddy Hill area and a second device was fired through a broken window into the house.
No one is reported as having been injured.
Mid Ulster detectives are appealing for witnessess and information.
Detective Sergeant Robinson said: "Shortly after 9:05pm it was reported two males arrived at a house, and that one of them may have been armed with a knife.
"When police arrived at the address, it was reported a petrol bomb had been thrown at the property, and a garden bench had been used to ram the front door, breaking a pane of glass. It was reported a second petrol bomb was thrown into the house.
"None of the occupants in the house, which included a man and a woman and young child and a baby, were injured, however this must have been a terrifying ordeal for them. This was a reckless attack which could have had a devastating impact, resulting in serious injury or worse.
"We are working to establish a motive for what happened and would appeal to anyone who was in the area last night at around 9pm and saw what happened, or anyone who may have been in the area earlier in the evening and saw anything out of the ordinary to call our detectives on 101, quoting reference number 1402 09/02/20."
Anyone with information can also call Crimestoppers, which is anonymous, on 0800 555 111.