A state income tax refund might be taxable if you deducted state income taxes on your federal tax return for the year you received the refund. Essentially, you would have deducted too much tax on your federal tax return, so the IRS requires you to add the excess amount back to income.
This prevents people from sending all of their money to the state so they can take a deduction on their federal tax return only to get it refunded later - basically making their income tax-free in a roundabout way.
If you didn't deduct state income taxes on your federal return, you will not need to pay tax on your state income tax refund.
A federal tax refund isn't considered income because you don't ever take a deduction for federal taxes paid like you can for state taxes paid.
[Edited 2/1 @ 4:40am]
