If the child inherits the house it is the child's house when legal title passes. If he was a joint tenant title passed on the decedent's death. if the house was left to him by Will, title passes when the Surrogate's court transfers title.  (I assume the child is age  18 or over and is not a minor.)If the estate is large enough to be subject to Federal Estate tax and/or New York State Estate Tax (and NY City Estate Tax) the estate tax must be paid. (The terms of the Will normally would specify how the tax is allocated across various beneficiaries.)When and if the home would be sold, its income tax basis would be the value of the house at the decedent's date of death.If you're asking about whether the house's assessed valuation for property tax purposes is redetermined at death,that's something you'd have to ask of a local real estate agent, local lawyer or (at the risk of triggering a reappraisal) the local taxing authorities.