I think I used the desktop and then e-filed. I am not sure of the distinction between desktop turbo tax and a different online option. I completed the filing online. At the time of my filing I printed a copy of my return and filing instructions. My Federal, Hawaii, and California return instructions all say that the Fed and State returns have been received electronically and there is nothing to mail. I received a Fed refund and Hawaii refund, but my turbotax instructions for California said there is no balance due nor a refund due: do not mail a payment or expect a refund from the Franchise Tax Board.
