After you file

I have a follow-up question:
I filed Federal as well as State tax using TurboTax. I believe Form 1040X is required to amend ONLY the federal tax in my case (Form 1040EZ). Please correct me if I am wrong.
If this, in fact, is the case then should I file only federal tax using SprintTax (as the new/amended return)?
Also, what happens to the State Tax? Are international students allowed to file state taxes using TurboTax?