Q. What do I put as the start date and end date. I have multiple start and end dates for both the states.
A. You usually don't enter any dates on a resident or non resident return.
If sounds like you may have indicated you were a part year resident. You don't want to do that.
For more background, see https://ttlc.intuit.com/community/state-taxes/discussion/residency-status-after-moving-from-wv-to-nc...
