Seablue, I believe that usually an out of district placement is only available (at district's expense) when the district has tried and failed to meet the child's needs, or when it's already crystal-clear that it can't do so. Every district will be different, but the norm is that they will want to serve your DD with the resources they have if at all possible.

Backing up several steps: this was a private eval, right? Has the district ever evaluated? If not, they HAVE to (by law) conduct an educational eval. All your letter has to do is to request that the district evaluate her, and list all the areas of concern. If you want to tell them you have this outside eval and diagnoses to share, it will speed things up considerably, but you are still looking at a process. The school is not entitled to diagnose anyone-- but they do have to make determinations of educational needs (as distinct from medical or other kinds).