This small and very wealthy nation has a relatively low incidence of serious crimes, and is one of the safest countries in the world for a traveler.
While it's not unheard of for a stolen car to make local news, visitors should not be too care-free with safety, petty crimes such as theft can take place. Take care of your personal possessions, particularly important documents like your passport.
Keep in mind the punishment for most criminal activity is fairly extreme here, so you shouldn't ever test the law in Brunei.
One of the reasons that crime is so low in Brunei is the severe punishments for criminal activity. Brunei is an Islamic country, and the legal system is based partly on Sharia Law, which in some circumstances also applies to visitors. So, while it is a far less restrictive Muslim state than many there are still social norms (including conservative standards of dress and behaviour) that should be respected by visitors.
Corporal punishment and a mandatory death penalty apply for many serious crimes like murder, kidnapping and drug offences. Robbery and visa offences are generally punished by caning. To avoid the cane don‘t overstay your visa. There are a few things that are illegal in Brunei that some foreigners may enjoy for example: consensual homosexual acts (of either sex), carrying guns or ammunition, pornography of any kind and convincing a mate to skip church – or in this case a Muslim person to neglect their religious duties.
A few other things to be aware of: smoking is banned in specific places, including government buildings, hospitals, recreational and educational centres, public transport and restaurants. Smoking in these areas can attract a fine.
It is also an offence to photograph prohibited places, including government and military infrastructure and equipment, places used by security forces and communications and civil infrastructure, and areas in the vicinity of such places. Best not to test this one as I suspect a fine will be the least of your problems if caught.
Can‘t get by without a drink? Don‘t worry, while Brunei is a ‘dry‘ country, private consumption of alcohol by non-Muslims is allowed. Tourists are permitted a duty-free allowance of two bottles of alcohol and 12 cans of beer per entry. Alcohol can be consumed with discretion at hotels and some restaurants and ‘by discretion‘ I mean that the bottle is kept under the table or out of sight as it is technically illegal for the restaurant to serve it to patrons.
Some cheaper restaurants may serve alcohol illegally using euphemisms like ‘special tea‘. Just use your common sense and discretion to avoid offending locals and drawing attention to your self.
Likewise, when visiting a mosque, use your common sense and respect local customs. All visitors should remove their shoes. Women should cover their heads and not have their knees or arms exposed and you should not pass in front of a person in prayer or touch the Koran.
Ramadan is a very special time for Muslims and showing some respect during this time will go a long way. During Ramadan, eating, drinking and smoking between sunrise and sunset is forbidden for Muslims. Though not illegal for non-Muslims, you should avoid these activities in public to avoid causing offence.
Finally, the Royal family retains a venerated status in Brunei. You should take care to not insult, make fun of or in any way denigrate them.
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