Rental depreciation: property tax improvement might be inaccurate?

Let's say I bought my house with 500K, and did the following improvements before converting it to rental:

 

- 100K remodel (county does not know)

- 250K home addition (county reassessed the value)

 

So the total cost of the house is 850K (let's assume this is the basis for depreciation, not FMV).

 

Now, the latest property bill is as follows:
- land 500K

- improvement 300K

 

If I just use it, TurboTax will use 850K * 3/8 = 319K as the value of my improvements and the basis for depreciation. However, the county's tax assessment does not know about the 100K remodel. My question is how I deal with this? Add 100K on top of the 300K? Ignore it?

 

EDIT: also this is CA, so with the prop 13 the tax assessment is normally not up to date esp wrt land value.

 

Thank you!