There's a filing with the Secretary of State in the state in which they are incorporated. This is public information.
Filings with the sec of state (at least in the states I’ve done it, and I expect it’s the same all over) don’t require provision of federal income tax information.
the state has no bearing on whether you are an S Corp. you file this request for S Corp status with the IRS after you create the corporation with the sec of state... the state is NOT involved