If my child is a Colorado resident, but going to school and working in Arizona, are they required to pay Arizona income tax?

See this:

Individual Income Tax Information | Arizona Department of Revenue (azdor.gov)

Nonresidents are subject to Arizona tax on any income earned from Arizona sources.

If your child's income exceeded the AZ filing threshold for non-residents, he/she must file a non-resident AZ tax return.

He/she must also file a CO tax return, since ALL the income of a CO resident is taxable by CO, regardless of its source.  But a credit may be taken on the CO tax return for the taxes paid to the non-resident state, thus eliminating double taxation.