Don't enter it as a contribution in the first place.  But enter it as "other taxes," if you're not already up to the $10K limit.  But make sure you do that for the right year, if it's one of those credits that applies to "donations" by April 18.  If you don't deduct it as a tax, make sure that adjustment is not made automatically on the state form (for example, way down at the bottom of AZ Form 321 is a place to indicate whether the amount was claimed as an itemized deduction). 

In Arizona, you can donate to a parochial school; a public school's "extracurricular activities;" or to a charity that helps local "working poor," and reduce your state tax dollar for dollar up to certain limits.  You don't gain anything, you just redirect your money.  I have started telling clients this is part of "Defund the Police."  They hate paying state income tax, but don't realize that much of the funds are shared with the cities that pay first responders.