In C#, that is technically not an array. An array is a collection of objects with the same type. What you have there, is an object and C# allows you to create anonymous objects. Like so:
var p = new {
user_auth = new {
user_name = "",
password = "",
encryption = "PLAIN"
},
application = "SugarCRM RestAPI Example"
};
if(p.user_auth.user_name == ""){
}