You will need to file a part-year NJ tax return for the time you lived/worked in NJ. WA has no state income tax so there will not be a WA return.
MOVED OR NEED TO FILE PART-YEAR STATE
https://ttlc.intuit.com/questions/1901560-how-do-i-file-if-i-moved-to-a-different-state-last-year
https://ttlc.intuit.com/turbotax-support/en-us/help-article/printers-printing/file-part-year-state-r...
ALLOCATE PART YEAR
https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/allocate-split-income-part-y...
https://ttlc.intuit.com/community/returns-and-forms/help/when-would-i-have-to-file-returns-in-more-t...
