Why was my federal refund deducted the amount to pay for state taxes owed when I already paid state taxes owed using my bank?

You cannot use your federal refund to pay your state taxes.  The IRS and State Governments have the ability to offset a refund to pay for certain past due debts.  You generally will receive a letter stating what the offset was for.   This is likely what happened.

The IRS provides a toll-free number, (800) 304-3107, to call for information about tax offsets. 

my federal was deducted the exact amount that i owed to state.