It depends on your income. Per the State of Arizona, you must make estimated payments if your Arizona gross income for both the prior year and the current taxable year exceeds $75,000 ($150,000 for married taxpayers filing a joint return). If you met the income threshold for the prior year, you must make estimated payments during the current year unless you are sure you will not meet the income threshold for the current year.
If you are required to make estimated tax payments, your payments must total either 90% of the tax due for the current year, or 100% of tax due for the prior year. Typically, you must make your payments in four equal installments. These installments are due on April 15th, June 15th, and September 15th of the current year and on January 15th of the next year.
For more information, please see the publication Arizona Individual Estimated Income Tax Payments.