Rhans really did answer your question, but here are some more details.
It is probably easier to check out of the BVI at Soapers Hole. Only the captain is required to go to the C & I office, on the second floor of the ferry terminal building, with the ship's papers. Just grab a mooring and dingy over.
The US rules require that all members of the crew go to the C & I office with passports and ship's papers. It is best to grab a mooring at Caneel Bay and dingy over to Cruz Bay where the C& I office is located at the ferry dock. You do not need to check out of the of the US Virgin Islands.
Upon returning to the BVI, you need to check back in - captain only with ship's papers. We usually check back in on Jost, but Soaper's is a bit closer - depends on your itenery.
In truth, we find the process to be a pain and spend the vast majority of our time in the BVI.