Based on the information you provided, you don't need to file a NJ tax return unless the move was temporary and you intend to return to NJ.
You earned all your 2016 income in WA, and you relocated before 01/01//2016.
Date
You Established Residency
The
date you choose as the first day of residency can coincide with one of the
following events:
You or your spouse arrived in the state or country
Your belongings arrived
You or your spouse started work
You started renting your new place
You purchased your new home
You or a family member enrolled in school
You or your spouse registered to vote
You or your spouse applied for a state driver's license
