Final answer:
The periodic performance evaluation for a Petty Officer Third Class in the United States Navy is due in March.
Step-by-step explanation:
The periodic performance evaluation for a Petty Officer Third Class in the United States Navy is due in March. Evaluations for junior enlisted personnel (E1-E3) are conducted in June and December, while evaluations for non-commissioned officers (E4-E6) such as Petty Officer Third Class (E4) are conducted in March and September according to the Navy's evaluation schedule. Therefore, the correct answer is the month of March.