I did my taxes last year and paid my state taxes but I recently got a paper in the mail saying I owe state taxes. Why is it saying I owe when I already paid?

Can you prove your paid your state taxes? If so, then send them the proof, be it a copy of the bank statement, credit card statement, or whatever.

It's also possible that you incorrectly paid your state taxes to another taxing authrority such as the IRS (which is federal). If you did that, then you haven't paid your state taxes and still owe your state along with any interest, fines and penalties that may have accumulated since the state tax payment deadline.

Oh Yeah. Also pay attention to what tax year the state is saying you didn't pay.

Your only proof of payment will be your own bank/credit card records.  I hope that you did not make the mistake of believing that a federal tax refund paid your state tax due, because that is not at all possible.