We have just used an English-speaking psychologist for an assessment of our son. In our case our health insurance will pay some of the cost (in Zurich around CHF 1500). I believe the school would normally refer children to the local eduction psychologist and this cost would be borne by the school, however the assessment would obviously be in the local language. This is probably the reason that your costs will be borne (hopefully) by your medical insurance as you need an English assessment.