There is only one file type that uses the .TT2013STATE extension:
TurboTax 2013 State Tax Form
State tax form used by TurboTax 2013, a tax preparation program; contains an official tax form for a specific state; may be filled out by the user within TurboTax and can be printed and mailed or filed electronically.
TurboTax Deluxe, Premier, and Home & Business editions include a free state return. You can download the state version you need directly within TurboTax by clicking thebutton where the state refund amount is displayed. The TT2013STATE files that are downloaded will automatically be loaded by the program, meaning you do not have to open them manually.
Updated: April 17, 2017