Since it seems many did not go to the link I posted like 10 pages ago, I'll include excerpts:
"In fact, your legal rights depend on whether the vessel is in port or within a country's territorial waters, where local law may apply, or on the high seas, where maritime law is in force. Few passengers are aware that the rules effectively change during their cruise, and when they find out what their rights are and aren't they are often surprised....According to the Bureau of Justice, 1 in every 1,000 people is raped or sexually assaulted on land each year; on cruise ships, there is only one alleged incident of sexual assault for every 100,000 passengers.
While legal experts don't necessarily dispute these statistics, they say that a closer look at the numbers suggests a deeper problem. For example, if a serious crime is committed at sea against an American citizen, the ship's security staff is supposed to report it to the F.B.I. But there are at least two exemptions: crimes against noncitizens are not included, and it is largely left up to the ship's security officers as to what constitutes a "serious" crime. Similarly, the statistics on assault and rape may be artificially low, according to legal experts. Many passengers are unwilling to report an assault because of the humiliating nature of the crime, and because they are uncertain of their legal status at sea.
The way in which the crimes are prosecuted can be different, too. "Crimes at sea are controlled by admiralty law," said Jeffrey Miller, a lawyer specializing in travel with the Columbia, Md., law firm of Lipshultz & Miller. "If the crime is committed in the territorial waters of a country or at port, then that country's laws and criminal justice system are in control," he said. "Thus a crime while in port in Cozumel or in Mexican waters would lead to Mexican justice or lack thereof."
While this may seem confusing in principle, it isn't in practice, according to the cruise lines. "In port, a crime is reported to local law enforcement," explained Tim Gallagher, a spokesman for Carnival Cruise Lines. At sea, the ship's security officer is notified of a crime. "The security officer would meet with the victim or the person reporting the crime, and take statements. It's our policy to report any crime that occurs where an American citizen is involved to the F.B.I.," he said.
If someone is believed to have committed a crime on the high seas, the captain can decide whether to incarcerate a suspect until the ship reaches home port or to remove that person at the next port of call even if it is in another country.
Mr. Gallagher said Carnival's standard operating procedure is to detain a suspect in a "serious" crime and hand the passenger over to the F.B.I. in the next port. Typically, he added, the kinds of passengers who are removed from the ship early are those who have engaged in unruly behavior.