One problem is that if your wife is going to file separate Head of Household, she cannot legally head of household if she lived with you for the last 6 months of the year. This is one potential problem that I see. If you two live together, then you need to file Married Filing Joint or Married filing Separate.
if she does qualify because of your absence from the home then she can file Head of Household. She would declare he filing status in the federal return and then this information will flow to your New York State return.(NYS) as a Head of household filer.
Also as you are preparing the NYS return, it will recognize that you are filing separately and will ask if you wish to itemize in your NYS as you are going through the return in Turbo Tax. Here is where you will indicate that you will itemize and she will itemize as well
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