No, these are not your HSA expenses.
The Arizona long-term health care savings accounts are intended to provide a vehicle for taxpayers to pay for long-term health care costs with pre-tax dollars. See the definition by the Arizona Legislature - http://www.azleg.gov/ars/43/01032.htm
Note the first line: "...Arizona resident taxpayer may subtract amounts contributed in cash during the taxable year to a long-term health care savings account as provided by this section to the extent that the contributions are included in the individual's federal adjusted gross income."
The issue here is that HSA expenditures are not included in your gross (taxable) income, therefore they cannot be used here on the Arizona return. To put it another way, you are already not being taxed on the HSA contributions and distributions, so to deduct these amounts again on the Arizona return would be double-dipping.