I received a K1 from an S corp in CA (I am a passive part owner). I lived in AZ for all of 2017. Do I need to file a CA state tax return and pay taxes on the K1 income?

A couple of comments:

1. First you need to determine if the S corp filed a composite return on your behalf.  A number of states provide for this filing, I have not researched to see if CA is one of the states. If the S corp did, then you do not need to file a CA return.  I would imagine if you received a K-1, no composite tax return was filed.  I would also assume that the S corporation would provide this information as well in either a shareholder cover letter of footnote.
2. Did the S corp withhold CA nonresident withholdings.  Most states have this requirement.  The pass-through entity will remit an estimated tax on behalf of the nonresident.  The nonresident shareholder will then claim this withholding when they file the applicable California tax return.
3. In addition, you need to look at what the CA filing threshold is.  You may be below the filing threshold, however, if the S corporation remitted withholding on your behalf, then you will need to determine if you owe any additional or if you are eligible for a refund.  In order to determine this you will need to complete a CA return form 540NR.

Thank you for the answer; it is very helpful.  For my federal returns, I had passive losses from previous years to negate the S corp income from 2017.  Do I still need to file California state taxes based on the 2017 S Corp income reported on the K1 without the benefit of carrying forward passive losses from the previous years?

deleted as duplicate response.

Federal and state tax law do not always mirror each other.  I have not researched CA law on whether or not you would still have the ability to offset current year income if you did not file in past years CA return(s) to report passive losses.
I would recommend you consult with a tax professional who would have this knowledge.
Also, just as an FYI, if you don't file a return in a particular state, the statute of limitations never starts.  So this means instead of a normal 3 or 4 year statute of limitation it is indefinite until you begin filing tax returns.