Final answer:
Needle decompression for a tension pneumothorax should be performed over the third rib at the second intercostal space along the mid-clavicular line.
Step-by-step explanation:
The most appropriate site for needle decompression in a patient who developed a tension pneumothorax after positive-pressure ventilation is over the third rib (i.e., second intercostal space) at the mid-clavicular line. This location provides the safest and most effective access point to relieve the pressure in the thoracic cavity by allowing air to escape, reestablishing the negative pressure needed for lung expansion. It is crucial to perform this procedure correctly to avoid complications such as damage to critical structures within the thorax.