Most of the rental properties in Belize are owned individually or by small homeowner's associations. Many properties are rented without contracts or rental agreements.
This can be good or bad, depending on how things go. For peace of mind, it might be a good idea to have a reputable Belizean attorney draft a lease agreement for you. (I would NOT recommend using a typical rental agreement that you can buy in an office supply store or get online.)
Since laws of this sort can be different from where you live, don't assume you know your rights and responsibilities. Having a rental agreement drafted should not be very expensive, but may help you avoid headaches if there is a disagreement of any kind down the road.
If you offer to pay for an attorney to draft a rental agreement and the property owner is not comfortable with it, that should be a red flag. In Belize, just like anywhere else, using your common sense in any situation will usually keep you out of trouble.