Current year is available up to 3-4 months back. There may be weekly indexes to consult which are more current. Go through each week. All indices are straight alphabetical order. Birth records are organized the same way.
Index includes last name, first name, date of death or birth and certificate number.
The borough of death is also listed. Common names are a problem, as there is no way of differentiating and no addresses are listed. Birth records include the maiden name of the mother. The death certificates themselves are not public records. They can only be obtained by next of kin.