Insp Michael Gregg said the house in Linen Green was searched after a vehicle "linked to the address made off at speed from a vehicle checkpoint".
The checkpoint had been set up at Prince William Road on Saturday night.
Officers are trying to find the driver who was not at the house when they obtained a warrant to search it.
As well as the cash and cannabis, police found quantities of suspected class A, class C and prescription drugs at the property.
Police have seized cannabis worth an estimated £60,000 and a sum of cash, understood to be in excess of £10,000, at a house in Lisburn, County Antrim.