My State taxes was amended and mailed. How does that work?

Yes, when you amend your tax return, you usually either owe some tax or get an additional refund. The original return and the amended return are processed separately.  

For example, you do your return, and it shows a $1,000 refund. After you e-file, you realize you have another W-2 form. You amend the return.  After you add the new W-2, it shows a $20 tax owed. 
 
In this case you will get the $1,000 refund from the original return, and you need to pay back $20 with the amendment. 
 

If that doesn't completely answer your question, respond back with more details about what you want to know.