First, yes, if you have income from a Trust earned in CA (since you received a K-1 541 from CA), then you will need to file a non-resident CA return and report the beneficiary income and use the adjustment amounts reported to you on the K-1 541 form.
Second, for your AZ return, if you entered the K-1 (Federal 1041) form on your federal return for the trust/estate that sent you the CA K-1541 form, then the K-1 income will flow through to your AZ return.
But, you will want to file the CA non-resident return first, so that you can get credit for paying taxes on the income in CA on your AZ return.
Here is more information on filing a non-resident return in TurboTax:
https://ttlc.intuit.com/replies/3302052
