No, you cannot both get a refund and owe tax. Whether you get get a refund is the net left after you pay tax. If you had tax withheld, that would be used to pay any tax you owe. The only way you'd get a refund would be if there were withheld taxes left over after paying what you owe and you would have to prepare your state tax return to know that for sure. In that case, the final result is you would be receiving a refund not paying tax.