As of today, there are no medical tests that determine whether or not a child has Autism
Spectrum Disorder (ASD). The medical tests that are recommended are to eliminate other possible diagnoses and to shed a greater light on the areas which the child is showing developmental delay.
The first step is to discuss concerns with your pediatrician. The doctor should then recommend that you have your child see an audiologist, a psychiatrist and a neurologist. Also, all states have an early intervention program for children with developmental delays called the Infant and Toddler Early Intervention Program (ITEIP). These services (including assessments and therapies) are usually free of charge, but require your pediatrician's referral.
Words of wisdom to parents: you will be seeing a series of physicians and your child will be having numerous tests and assessments done. As stressful as this can be for both you and your child, it is important that you follow through with all the recommended testing. Primarily, you want to make sure that there is not something else going on (such as hearing loss) and you also want to know the whole diagnostic picture. Find physicians who you are comfortable with and that are good diagnosticians. This is why speaking with others about who their child has seen and doing your research is important. All of this will help you further on down the road as you make critical decisions on which therapies and treatments will best help you child.