If your state has an income tax, yes, it is done separately from the Federal filing. Also, find out if you have a city or local income tax. Where I live, some communities have a 1 or 2 percent income tax for residents.
When I lived in Vermont, I had to file and send separate returns for Federal and State taxes.
Having spent most of my adult life either in WA or NH, I haven’t filed State taxes in years though :D