Basically, the valuation by a certified appraiser is always best. But not necessary in all cases. Just tell the appraiser you need the valuation to reflect it's value on the date the original owner passed. If within the last year, it won't be that much different if there's any difference at all.
Just don't use the tax bill as justification for property value. That only determines and sets tax value and is typically 30% or more lower than it's actual fair market sale value.
