Can I file state tax from a different site than where I filed my federal

Kind-of yes..

If you filed Federal with TTX, and it was accepted.....and If you didn't file your state with TTX (or filed it, but it was rejected).

1) Then, you can sometimes go to your state's tax website to file just the state.  Some, but not all states, have their own Online procedures available to file that state's taxes for simple state tax returns.

2)  Cany you go to another software provider to just file the state?   Only with difficulty.  You'd have to (potentially) buy their whole Federal/state package.  Prepare the Federal to "exactly match" the Federal forms youa lready filed with TTX....then finish state....then print out the state forms and mail them in.  (IF you want to e-file the state, it msut unusually be done in the same software package that the Federal was e-filed in)