What is the tax liability on sale of inherited property that was transferred in my name?

Assuming it is a capital asset, the basis for the property is "stepped up" to the Fair Market Value (FMV) of the property on the date of the death of the original owner, or, at the estate's option, the FMV on the date six months after the original owner's death.

Your tax would be based on the difference between that FMV and what you actually got when you sell it. If you sold it for a loss, then you cannot claim the loss unless the asset is an equity (stock or bond).