Federal and state refunds come from completely separate entities,There is no rule as to which one will come first or how much time there will be between their arrivals.
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Your "refund" is what you might be expecting to get back. i,e,....That you might get back...might.
Check the following link directly with NC...note that they are just starting to send them out the week of 18 March (this week), so yours could be several weeks away, with thousands of others issued before your own: