My son's mother and I are not married and live apart. We had our son in Michigan and now live in Tennesse. She will not tell me where my son lives currently. Can she do this?

Who has custody of your son? Has a visitation order been established? If you really want to know where your so is living and she refuses to tell you then you should file a motion in Family Court to get an order of visitation and/or joint custody. Then she'll have to reveal where he's living.