You'll need to file a motion to reject the report if indeed you did not sign the Referee stipulation. If you signed the stipulation, then your only recourse is to appeal to the Appellate Division.
I believe that a letter is meaningless. There are rules and statutory procedures on how to deal with a Referre's decision and you can't circumvent them with a letter. Your adversary is entitled to a motion on notice or an Order To Show Cause m
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No, writing letters to a judge with objections or legal arguments is not appropriate. If there are objections to a report they should be handled through the appropriate process.
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Proper procedure would be for you to file a motion objecting to the report and detailing your objections to the conclusions the Referee reached. If you're representing yourself (though not advisable), I'd recommend a trip to the Supreme Court's Law Library for the forms. Call a NYC Divorce attorney for a consult.
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