Is there a tax break or deduction for Arizona state retirement system (ASRS)contributions?

Yes.  "ASRS contribution rate actually consists of two main parts: the “Pension and Health Insurance Benefit” rate, which is a pre-tax deduction from your paycheck, and the “Long Term Disability Income Plan” rate, which is a post-tax deduction. If you look at your paystub, the pre-tax deduction is listed as “ASRSRET” while the post-tax deduction is labeled “ASRS LTD.” 

The immediate advantage of having most of your contributions deducted pre-tax is that it lowers the taxable income of your paycheck. Fewer taxes are taken out of your paycheck by paying contributions pre-tax than if the same percentage of contributions were taken out of your paycheck post-tax."

Similar to most pensions, taxes are paid when you eventually begin to withdraw funds in retirement.

For more information: Arizona State Retirement System