The answer depends on how the product thawed and for how long. Freezing does not kill bacteria, it only stops them; USDA FSIS notes that once food thaws, microbes carry on multiplying at about the same rate as on fresh food. So the decision rests on how long the product spent above 4 °C.

Product conditionDecision (USDA FSIS)
Still has ice crystals or at 4 °C or belowCan be refrozen
Thawed in the refrigeratorCan be refrozen without cooking, quality drops
Thawed in cold water or a microwaveCook first, then freeze
Above 4 °C for more than 2 hoursDo not refreeze, discard

Commercial quick-frozen food is held to a stricter rule. Turkish Food Codex communiqué 2014/47 requires every point of the product to stay at -18 °C or below at all times, allows brief rises of no more than 3 °C in transport, and makes 'do not refreeze after thawing' a mandatory label statement. A lot that went beyond that limit no longer meets the definition's requirement of a continuously maintained -18 °C, and refreezing does not restore it.