The incident occurred the weekend before last.
Police have issued an appeal for witnesses.
Police say they investigating a report of damage caused to a grave at a cemetery on the Cumber Road in Claudy sometime between the afternoon of Saturday, December 11 and 12.30pm on Sunday, December 12.
Anyone with information about the incident or who saw suspicious activity in the area is asked to call police on 101 quoting reference 1071, 12/12/21
A report can also be made using the online reporting form via www.psni.police.uk/makeareport . Alternatively, information can be provided to crime stoppers anonymously on 0800 555 111 or online at www.crimestoppers-uk.org