Health professionals. There is no single test to test for dyslexia. Ways to definitively diagnose dyslexia are elusive. Dyslexia is determined by the presence or absence of its various symptoms. Comprehensive testing provides a way of measuring these symptoms. Educational psychologists are adept at diagnosing along with psychiatrists/psychologists.
School or private. Most insurance plans dont cover this. It can take time to get an eval approved by the school in the current "response to intervention" system, which is akin to trial and error. This can let kids languish until a diagnostic assessment would be done and delay early intervention that is targeted based on psych tesitng: http://cpancf.Com/articles_files/dyslexiareadingdisorder.Asp.