Here is a link to the Animal Hospital of St. Maarten. You could download the application for the import permit on their website. Follow the instructions. You'll basically need the import permit along with your USDA health certificate and rabies vaccination certificate to enter St. Maarten.

Coming back to the US, you will need nothing, although the Airline you are travelling on might require an health certificate saying your pet is ok to travel, check your airlines requirement for details. We brought back a cat 3 years ago. Coming back in to the US, CBP told us they don't need any paperwork for cats. They only check paperwork on dogs.