Do I also amend my state taxes?

I did my taxes and filed my federal electronically.  I had to mail my state taxes in, but since I owed a little, I just haven’t gotten around to doing that yet.  Today I got a 1099 in the mail for some money I forgot was going to be taxed. So my questions is, can I go in and update my tax file and just mail in the updated original d400 form to the state?  I’d then turn around and do an amendment on my filed federal return and mail that to them.   

So basically my federal tax form would be the 1040x, but my state form would just be the normal one since I had never mailed it originally.   

Is this ok, or should I just file my original state from two weeks and then just turn around and amend that to just to mail again?