I've had to obtain Police Checks for either residency or citizenship applications for 4 countries, including Belize (residency).
The request has always been for the check to be done at the police station in the place (usually the nearest city) where you have lived for the previous 6 months.
You said that you're applying for Belizean citizenship, so I assume you are already a permanent resident of Belize.
But are you living in Belize? If so, I'd say the check would be done in Belize. Ask at your nearest police station; if they can't do it there, they'll tell you where to go to get it done.