It depends. According to this Turbo Tax post, if you electronically filed your federal return, you do not need to send in the federal return with the state return. I would rely on the advice given to you on the phone by the NYS representative.
If you do send in the federal with the state return, I wouldn't guarantee it will be returned to you in the mail. If you send one in, make sure you another copy handy somewhere either printed on downloaded to your computer.
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