Most of the offenses against visitors are petty theft. Be smart and don't bring a lot of valuables. Anything you leave in your room should be hidden or locked up if there is a safe box. DO NOT walk the beach (or any dark areas) at night by yourself. There are many places there for perps to hide.
That said, there is not a lot of crime on CC. If you act smartly and do not leave yourself open as a victim, you will be safe. CC is definitely a quiet, warm, peaceful and safe island, enjoy!