The incident happened at a house in the Crossglebe area of Cookstown on Saturday night (February 20th)
A release from the PSNI says the incident was reported to them at around 9.55 pm.
At that stage police were told the petrol bomb had been thrown at the front of the property five minutes earlier.
Police said that a female occupant heard a loud bang and saw flames at the window, when she went to the front of the house she observed a masked man standing next to a car parked outside.
The male dropped a bottle he had been holding and ran off.
Police added that two occupants who were in the property at the time of the incident were uninjured.
Police are working to establish a motive for the attack and would also like to hear from anyone with information.
They are particularly keen to hear from anyone who was in the area and who have seen a male fleeing the scene.
Detectives can be contacted by calling 101, quoting reference 1908 20/02/21.
You can also submit a report online using our non-emergency reporting form via http://www.psni.police.uk/makeareport/
Alternatively, you can also contact Crimestoppers anonymously on 0800 555 111 or online at http://crimestoppers-uk.org//
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