Yes, the gain exclusion rules is true for NY.
When did you inherit the house? Did you inherit the entire house? Did you own and live in the house for atleast 2 years before selling the house?
If you have owned and lived in the house for atleast 2 years after inheriting than you can claim exclusion on the gain on sale of the house subject to the limitation that you had described in the post.
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Please note: This advice is provided with the understanding that all the relevant facts have been provided by you. Any change in facts might affect the advice given and hence may not be relied on in such cases. Nothing contained in this reply was intended or written to be used, can be used by any taxpayer, or may be relied upon or used by any taxpayer for the purposes of avoiding penalties that may be imposed on the taxpayer under the Internal Revenue Code of 1986, as amended.
Yes, if you gain is under $250K or $500K(if Married filing jointly) than it will not be taxable. You will file your regular tax form and exclude the home sale.