Police are treating an arson attack, in which a shed and oil tank were destroyed, as a racially motivated hate crime.
It happened in the early hours of Saturday morning on Jacksonville Road in Moygashel.
A man, his partner and two young children escaped injury but police have described the attack as 'extremely traumatic' for those involved.
Inspector Joanne Gibson said: "This was a cowardly attack on a family who should be able to feel safe in their own home with their young children. No-one has the right to take this away from anyone.
“I would appeal to anyone who noticed any suspicious activity in this area around the time of the incident to contact detectives at Cookstown on the non-emergency number 101, quoting reference 219 30/11/19."