Extension over existing patio.
 

I have a 20x10 concrete patio in my backyard. My question is if i add an extension over that footprint of the patio would they get me good with taxes after it is built? Being it is over an existing "footprint" of the property.

If by "extension" - you mean an "addition".
You're increasing the "livable" space of your house.
That's going to be "taxable" (property taxes).

You should consider permits, on this project.
How thick is the patio? -
Is it on any kind of foundation?
A patio, is usually not, considered part of the foot-print of the house.

rossfingal

This is something you will realy need to ask your local building authority about. Every area of the country (US) has different ways of assesing property. For example My town does not consider a covered patio to be "part of the house" but the neighboring city does and taxes it as such.