Well, sorta. Both states spend more money than they take in, but California's problem is that it's committed to too many programs (pension promises and ill-advised propositions didn't help), while Arizona taxes too little for programs already on the books. They both result in monster budget deficits, according to a Brookings Institution paper, but at least California has a tax system that will generate more revenue once the recovery takes hold.
Unlike Arizona, California suffers from more of a spending problem than a revenue problem, a result of permanent spending increases that were introduced during years of economic expansion. For example, the state significantly increased spending on education during the 1990s as the dot-com boom boosted the economy and personal income tax revenues; further spending increases were implemented in the relatively healthy years of the mid-2000s. Voter mandates and other institutional constraints have further strained budgeting in California. California's Proposition 98--the Classroom Instructional Improvement and Accountability Act passed in 1988--requires that nearly one-half of all new revenue be dedicated to support schools. While it is hard to argue against funding for education, the fact is that Proposition 98 reduces lawmakers' ability to address the state's structural deficit even as it hampers its ability to fund other programs.
More of California's problems are attributed to cyclical problems (lower tax revenues related to a down economy) than structural ones (long-term budget gaps that can't be made up even when times get better).