You'll have to clarify what you're asking for. As far as I know, there's no such thing as an "out of state" property tax. There are different property taxes assessed in each state, whether you're living in the property or not.
You can get a very good estimate of what your property tax will be on a specific address from the Pinellas County Tax Collector's website. Also look on the left column and click on how to estimate taxes. There are Homestead exemptions and "Save our Homes" discounts so you cannot be assured your property taxes will be the same as the current owners are paying.
Your Realtor can assist you, too.
If you're not yet working with a Realtor, I or one of my team members can offer to help you.
All the best,
Alma Rose Kee PA
Future Home Realty