If I am enrolled in a high deductible health plan with an HSA, can I deduct my health expenses on my state income tax (not federal) and still seek reimbursement later?

I do not know which state you are referring to, but I would think that it highly unlikely that you could "double-dip" on the state return either.

In fact, it is so unlikely that I don't think it's worth investigating, even when I know what state it is.

Thank you. That was the guy-check I was looking for. 

you could but it would have to be done for both federal and state. Getting reimbursed from the HSA could be a recovery that becomes taxable income to the extent you benefited from the deduction.