True. The new federal idea 2004 (individuals with disabilities education act) states that the district in which the private school resides is the district that needs to do the testing. Find out what school district the child resides in and contact the district. The big problem you may run into is the lack of interventions. If the school does not have enough interventions then the district may say that enough hasn't been done. In order for a child to get tested in most school district, the school is required to keep a list of various interventions and the outcomes. If, after many interventions, the child is still having difficulty then the child usually has an evaluation.
So, your first step is to call the local school district. If they are confused, contact the state department of education. You shouldn't have to pay out of your own pocket for an evaluation.
Good luck and pm me if you want specific information. This is my field of expertise.