Tax assessment values are not used for, and can not be used for depreciation. The only thing the program uses your tax assessed values for, is to determine what percentage of your cost basis will be allocated to the land, and what percentage to the structure. That's it.
For depreciation, you will use the "LOWER" of
1. What you paid for the property when you originally purchased it, or;
2. The FMV of the property on the date you converted it to a rental.
It is not common for the value of the property on the date you converted it to a rental, to be less than what you originally paid for it.
When setting up the asset:
COST: this is what you paid for the property in total, when you originally purchased it. To this amount you will add what "YOU" paid for any property improvements completed during the time you owned it. It does not matter if that property improvement was before you converted to a rental. It still adds "real" value to the property.
COST OF LAND: The portion of the amount in the COST box, that is allocated to the land. Typically, the program will use your tax values to determine what percentage of COST to enter in the COST OF LAND box.
Since you are renting only a part of your residence, it's important to confirm beyond any doubt that the amount of depreciation taken for that first year is correct. Because of programming limits, my bet is it will be wrong for that first year.
To confirm this, see IRS publication 946 at https://www.irs.gov/pub/irs-pdf/p946.pdf use the MACRS worksheet that starts on page 37. The table that will apply is table A-6 on page 72.
