Yes, it is possible. The tax owed to your state depends on how much was withheld and the amount of taxes calculated on your state return. So if your state withholding was too little, but your Federal withholding was closer to your actual estimated tax payment, then you may end up with a larger amount of tax due for state than for Federal return.
In fact, in some cases, one can get a refund from a Federal tax return while having tax owed on the state return.