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