The U. S. Dept. of Agriculture (USDA) advises:
Once food is thawed in the refrigerator, it is safe to refreeze it without cooking, although there may be a loss of quality due to the moisture lost through thawing. After cooking raw foods which were previously frozen, it is safe to freeze the cooked foods. If previously cooked foods are thawed in the refrigerator, you may refreeze the unused portion. Freeze leftovers within 3-4 days. Do not refreeze any foods left outside the refrigerator longer than 2 hours; 1 hour in temperatures above 90 °F.
If you purchase previously frozen meat, poultry or fish at a retail store, you can refreeze if it has been handled properly, according to USDA.
DO NOT thaw meat at room temperature, such as on the kitchen counter.
Safety will depend on whether the raw product was handled properly before it was frozen, refrozen shortly after it was thawed, cooked to a safe temperature when it is eaten and handled safely if there are any leftovers.
Freezing and Food Safety: Food Safety and Inspection Service (FSIS), United States Department of Agriculture