Get your taxes done using TurboTax

To clarify a bit further -

Switch from Step-by-Step to Forms Mode.

Scroll down the Forms in My Return list to your state return.

Right after the State-1040 form, there should be Info Worksheet.  Click.

In Part VII you have the options (yes/no) to select -

    Use direct deposit for any state refund

    Use direct debit for state tax payment

    Use direct deposit for any city tax refund

    Use direct debit for city tax due

Just below, you will enter the bank info.