The probe was sparked after an anonymous caller contacted the MLA’s Dunloy office claiming a device had been left at the family home.
Police have now tasked Army Technical Officers to the property.
A robot will be used to examine the home for any suspicious objects.
Mr McKay said it was not the first time he had been threatened.
“But once someone brings your home and your family into such an attack then obviously it does concern me greatly,” he said.