No, Belize will not make you pay taxes on money you earn outside of Belize. You could have passive income from a rental property or income from a US consulting or internet business and the money could come to you in Belize tax free because it is not earned income in Belize. Please check with a lawyer for accurate information pertinent to you.
If you have income in the States you could leave your money there, transfer your money to a Belize money exchanger or you could put it in an offshore account if you’re not a citizen. You cannot have an offshore account if you are a citizen of Belize. On a side note, you cannot have more than $10,000BZ on you at any one time. So you wouldn’t want to go to your money exchanger and have them convert US $10,000 into BZ $20,000 because if you get involved in a traffic incident or are stopped by the police for any reason and they discover it, they can confiscate it.
(Caye Caulker, Belize, pictured.)