New York State's estate tax is calculated using the tax table provided on Form ET706. There are multiple versions of Form ET-706.In New York State, the Surrogate's Court decides what happens to a person's property when that person dies. Administration is the process where the Surrogate's Court officially gives out Letters of Administration to a qualified distributee (heir) of the Decedent. Obtain your letters of testamentary in New York with ease. File the final income tax returns of a deceased person for current and prior years, pay any balance due and claim the refund. File an estate income tax return.