[BjoernKW]

Theoretically, yes.

However, it seems to be a more or less open secret (from a friend of mine who works in the industry) that investigations won't be conducted as diligently as if the crime had happened on land.

Part of the reason for that is that it's difficult to secure evidence after several days or even weeks and the staff on board or the police in the next port often isn't qualified to do so.

Another contributing factor seems to be that cruise ship operators don't want any hassle or negative press and therefore push for investigations to be dealt with swiftly and silently.