To start: most commonly a state will require copies of all of an organization’s founding documents [i.e., Articles of Incorporation, IRS Determination Letter, and Bylaws], a copy of the most recently filed IRS Form 990 and corresponding audited financial statements, and the state’s registration form.
To renew annually: the state’s renewal form, IRS 990 filing and audited financials for the proceeding year.
Special contracts: If the nonprofit organization has any contracts in place with fundraising consultants, professional solicitors, or commercial co-venturers1, a copy of the contracts must be submitted in the registration package.
Of course, each registration application requires the filing fee which varies among the states
1Note: A commercial co-venturer is a for-profit cause marketing sponsor (e.g., McDonalds, Pepsi, Nike, etc).