Crooks have damaged the window of a house in Barpath, Kilsyth.
Police say the damage was caused because they attempted to force entry into the premises.
The incident is believed to have happened between 2.30am and 3.30am on Wednesday, May 29.
A number of fencing slats have been stolen from a fencing company in Kilsyth.
Perimeter fencing was damaged in the incident before the theft took place.
The incident happened between 4.30 on Wednesday, May 29 and 8am the following day.
Witnesses to any of these incidents should contact Cumbernauld Police Office on 01236 503 900.