The property taxes are sky high, yes, but they most definitely do not exempt the rich. There is no state income tax. I wouldn’t call the state’s general tax structure progressive or regressive.
That said, I don't think it's enough to just look at one tax. We have to consider taxes and regulations as a whole to understand whether a place is overall regressive or not. This leaves room for different implementations of tax policy which if done correctly will benefit the people.