I would get in touch with a child psychologist who has knowledge and worked with children with selective mutism.
My best friends DD was potentially considered to have this. Because of issues with her X-DH and the child's refusal to speak to people (other than parent or close family or those she was comfortable with), she got the child into a psychologist. In the end, it was a diagnosis of social anxiety bordering on general anxiety.
She was never offered medication, but rather counseling on a weekly basis. Her DD is doing much better now. She is still going to counseling about 2 times a month. She is now talking in school and talking to her teachers. She was first diagnosed in Kinder and is currently in 2nd grade. Her speaking has negatively affected her education in that she does not do well with verbal learning, she is a purely visual learner. As a result, on standardized testing she does horrible in a lot of stuff, but she is visually gifted after testing.