Do I have to amend state return after 1040x ? No change in tax due

Hi, I filed 1040x to reflect some deductions so my income has reduced.

I file for multiple states and one of them (OH) show no change in tax amount after 1040x.

But total income is different. Should I still file state amendment for OH though there is not change in tax amount.

I read the instructions and it looks like I don't have to file because it does not cause any change in my tax due.

I just wanted to make sure because the final PDF contains OH state amendment forms...