Determine whether the string is JSONObject or JSONArray

Use JSONTokener.
 JSONTokener.nextValue() will give an object which can then be dynamically cast to the appropriate type.
Object json = new JSONTokener(jsonResponse).nextValue();
if(json instanceof JSONObject){
    JSONObject jsonObject = (JSONObject)json;
    //further actions on jsonObjects
    //...
}else if (json instanceof JSONArray){
    JSONArray jsonArray = (JSONArray)json;
    //further actions on jsonArray
    //...
}