According to the U.S. Department of Health & Human Services, foods cannot be safely refrozen after defrosting when held above 40 degrees Fahrenheit for two hours or longer. However some foods that can be safely refrozen are hard cheeses, breads and bagels, fruit and fruit juices, and nuts.
Vegetables and vegetable juices can be refrozen unless they were held at 40 degrees Fahrenheit for six hours or more. Foods that are partially thawed are safe to refreeze, however the texture and taste could be affected. The department also recommends never to taste the food to determine whether it is safe and to discard any frozen food that comes in contact with raw meat juices.