The instructions for form 321 are quite specific - contributions to qualifying charitable organizations eligible for the Charitable Tax Credit (which is different from a deduction) must be in cash.

However, any contributions made on the federal return for Schedule A (Itemized Deductions) will still be deductible (carried automatically from the federal return), but just not eligible for the Charitable Tax Credit in Arizona.

[Edited 3/17/2020 3:07 pm CDT - removed out of date link]