It was revealed earlier this week that Lyle Kirk on Newark Street had been targeted.
A separate incident at St John's Scottish Episcopal Church is being probed.
Police say the building on Union Street was targeted some time between January 26 and February 1.
Area commander Chief Inspector Paul Cameron says additional officers are on patrol around churches and places of worship as a result .
He added: "These are despicable incidents targeting local church buildings.
"I would appeal to our communities to report anyone acting suspicious around our places of worship."
Anyone with dashcam or CCTV footage, or who has any other information, should call 101 or contact Crimestoppers on 0800 555 111.