Three men reportedly forced their way into a house in the Moor Road area of the Co Tyrone town at around 8pm on Tuesday and threatened a 35-year-old man.
He is a witness in a court case.
The gang ran off after being challenged by the man, who was not physically injured in the incident, and whose wife and children were at home at the time.
Four men, aged 29, 31, 42 and 45, were arrested in Coalisland on Wednesday morning and are now being questioned at Antrim Serious Crime Suite.
Police have appealed for information about the movements of silver Volvo S70 car, which is believed travelled to Coalisland from the Belfast area.
It had an Eagle taxi sign on its roof and the registration number V 620 EWB.
Anyone who saw the vehicle between 6pm in Belfast and midnight in Coalisland, particularly in the Moor Road and Washingbay Road areas, can contact detectives on 028 9180 1507.