Most crimes in Liberia tend to be opportunity-based, and usually occur at night. The UN has both the UN Mission, UNMIL, and UN Police, UNPOL, in the area, but they have no authority to arrest and don't carry weapons, making them largely useless. In other words, don't assume you're safe.
The Liberian National police do have a strong presence in Monrovia, but it has limited resources and its presence outside of Monrovia is small.
The police can actually be a bit of a problem. While they're nowhere near as corrupt as they used to be, some members of the police force still stop foreign travelers and not release them until some form of bribe has been delivered, so watch out for that.
Make sure you have a copy of your passport on you at all times, so if local authorities do decide to question you, you have readily available proof of identity and nationality.
Liberia is one of those places where you need to be on your guard almost everywhere. Monrovia gets much worse at night, but it can be dangerous during the day as well.
Areas occupied and frequented by foreigners aren't regarded as safe, even though they are (marginally) safer than other areas.
Mamba Point and Sinkor in Monrovia, where foreigners tend to stay, have had many reported incidents of mugging, assault and other crimes. Foreign workers aren't safe in their locals either, and burglaries do occur in hotels.
West Point, one of the many slum areas in the capital, Monrovia is also one of the most dangerous places in Liberia. In addition to the prevalent crime, diseases like tuberculosis, gastro and more frequently infect the 80,000 residents which live there, no thanks to the poor sanitation conditions present.
Theft and armed extortion has happened in taxis and really, if the dilapidated state of the taxis in Monrovia wasn't enough to make you steer clear, the fact that taxi drivers tend to rob foreigners should be.
It's a good idea to stay away from public transportation altogether.
Don't travel outside of Monrovia at night. The roads are absolutely terrible and the countryside has more than enough criminals with automatic weapons who won't hesitate to use them.
Sadly, Liberia has one of the highest rates of rape in the entire world. There have been numerous incidents of rape and attempted rape on expatriate women, many of whom worked for charity organizations of the UN.
If you're female, don't believe that because you're there to help, you won't be harmed. In fact, women are advised not to travel to Liberia at all.
Liberia has many mass escapes from its prisons, and those escapees are rarely recaptured.
This means there are a lot of men more desperate than usual, and are highly likely to be armed and looking for a getaway vehicle. If you're approached by strangers, while driving, be very careful and make sure your windows are up and the doors locked.
This especially applies both in high population areas, and when driving off the main roads.
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