USDA classifies rabbits, like bison, as a "non-amenable" species, which means that they do not have to be processed under USDA inspection, although there are USDA inspected facilities that process rabbits.
However, anyone who processes any sort of food for sale -- whether salsa or jam or rabbits -- will need a license from the agency (state or county level) responsible for that. The license will require the producer-processor to follow basic sanitation requirements so the foods are safe. This could be the county health department, acting as a proxy for the state health department. Start by calling your county health department to find out.
