Federal special ed law (called IDEA) gives you the right to request an independent evaluation from the evaluator of your choice (as long as they have the proper credentials) at the district expense if you disagree with the evaluation for any reason. You do not have to state why you disagree.
Typically, private evaluations are more comprehensive and diagnostic than school evaluations. Schools have an inherent bias against finding issues and making strong recommendations. Sometimes, a private evaluation can shed more light. One caution - districts need only to "consider" outside evaluations. And considering is defined differently from school to school. Some thing that merely reading the report and casting it aside is enough. However, your best chance of getting some help and understanding your child's needs and profile will come with a good independent evaluation by an experienced neuropsychologist.
To read more about independent evaluations and your rights under special ed law go to:
http://www.wrightslaw.com/info/test.index.htmhttp://www.ldonline.org/legalbriefs/c672/You should also read your state's "procedural safeguards" which should explain any additional protections afforded by NY state. The district should have given you a written copy (this is the law) and it should be posted on the NY DOE website.