When amending your Federal Return, continue on to your State and indicate you 'want to amend'.
The info you changed in your Federal return will flow into your State Return. If it changes your State Refund, then go ahead and finish amending your State.
If not, you don't need to Amend your State Return.
Don't submit an Amended Return until you have received your Refund from your originally filed return.
Click this link for instructions on How to Amend Your Return.