In most states, no. While a handful of states have a simple, one- or two-page form that must be prepared, California is the only state that requires a separate application process rivaling the one required by the IRS. In California, federal tax-exemption does not eliminate state income tax liability until approval is received from the California Franchise Tax Board.
Organizations filing Form 1023-EZ are also required to file the entirety of the separate application to the California Franchise Tax Board.
All Foundation Group 501(c)(3) formation clients located in California receive assistance with the Franchise Tax Board process along with their federal work (this excludes Foundation Group Express-level clients).