Do I need to amend my federal return if there are changes to state return?

I have a quick clarification about amending my federal return -

 

I filed my federal return and then when I filing my state return I had multiple states to cover, but realized that I was missed entering the info for all the states, i.e., live in State A and work in State B so I had all the State A info but missed to enter all the State B W-2 info before I filed the federal return. 

 

However, I was able to catch the gap before filing the state taxes, so wanted to check do I need to re-file my federal showing the updates to tax withholding for State B? 

 

FYI - I did not owe any taxes for either Federal or the states.