The Department of Agriculture are the folks that oversee the animal permits, see their website's page on the topic at http://www.vifresh.com/vitnary.php.
Here is what they have for dogs:
"*** DOGS ***
All dogs upon entering the Virgin Islands shall be accompanied by an official health certificate stating that the animal did not originate from an area quarantined for rabies. All dogs must have been vaccinated for rabies within 6 months prior to the date of shipment except those dogs less than 12 weeks old. The certificate of vaccination for rabies must be attached to the official health certificate. No import permit is required."
It doesn't detail who fills out the certificate. You might call the Dept of Agriculture, and ask for Dr. Bethany Bradford, the director of vet services - she should be able to clear up exactly what your vet needs to provide you with. (Their number is at the top of the same webpage listed above with the regulations.)
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