A number of flats in the Moyraverty Centre in Craigavon had racist graffiti painted on them.
Police are treating this incident as a hate crime.
The incident occurred yesterday morning (Thursday) sometime between 4am and 7:10am.
The graffiti has subsequently been removed from the properties.
Police are also investigating a report of criminal damage which happened in the early hours of this morning (Friday) at the same location.
A substance was thrown at the front door of a flat just after midnight.
Constable Young said police are investigating a link between both incidents, which are being treated as hate crimes.
“Enquiries are continuing and we would appeal to anyone with any information to contact police in Lurgan on 101, quoting reference number 292 24/1/19.
“Alternatively, information can also be provided to the independent charity Crimestoppers on 0800 555 111 which is 100% anonymous and gives people the power to speak up and stop crime,” he added.