In North Carolina, if you've been laid off and received severance pay, you likely do not need to pay North Carolina State Income Tax on the severance amount up to $35,000. The way it works is you enter your severance as a deduction on line 43 on page 3 of your Form D-400.
Check out the North Carolina Department of Revenue statement on the subject by clicking here.
Also, if you received severance, you are typically not able to receive unemployment compensation from North Carolina until AFTER your severance period, UNLESS you register for certain education courses. For example, if you made $5,000 per month and received $10,000 severance, you typically can not draw unemployment compensation for 2 months. However, you may be able to draw unemployment simultaneously if you register for a class. Check with your local North Carolina Division of Employment Security office to verify which classes qualify.