Graffiti was also painted on a wall of the building
PSNI officers are investigating two incidents in Newtownards being treated as hate crimes.
They happened Wednesday and early Thursday morning.
At around 11:15pm on Wednesday night, a report was made to police that a pig's head had been placed on the doorstep of a building.
Graffiti was also painted on a wall of that same building, believed to be an Islamic centre.
While shortly after 1.00am Thursday, it was reported that graffiti was also been painted on the wall of a building in the Castle Street area.
The PSNI have confirmed both these incidents are being treated as hate crimes, and an investigation is underway.
They are appealing to anyone with information about either incident to contact police.