I've been through a very similar situation when my oldest was in Kindergarten. He also would "refuse" to answer. And by golly, you could NOT make him. He was found to a language processing 'disorder' (for lack of a better word).
He spent time each week with a speech and language therapist provided by the school, at school. (the evaluation was done through school)
They worked on goals such as: establishing appropriate eye contact with listener/speaker, decreasing response time after being asked a question, expected to comment when appropriate.respond to yes/no questions. They also worked on initiating greetings/farewells upon entering/leaving a room, asking for assistance to complete a task when directions were not understood or missed. His difficulties were in the area of Pragmatic Language.
--he is now 25 years old and still tends to be quiet, answers only when directly spoke to (except when aggravating his brothers!), has a hard time asking questions-but we've learned his 'signals. Prefers not to use the phone
BUT he has graduated, has a good job, also owns his own house, has to deal with 'homeowner' things himself-and he does. And is (from what I hear) much more talkative around friends than family!
I hope this helps, it's been so long ago that I had to dig out the evaluation papers from back then, and sometimes I forget all that we went through.
You may contact me directly if you'd like more info/details. I have another son that has some language processing issues also. I'll do my best to help.