How To Open Multiple SqlConnection Objects In A SqlServer Project

I have a sql server project where I have added 1 stored procedure (named StoredProcedure1) and 1 class (named MyClass). MyClass has two functions Func1() and Func2(). The stored procedure simply instantiates MyClass and calls Func1().

Func1() creates a SqlConnection object using "context connection=true" - opens the connection and then calls Func2(). Func2() also creates a SqlConnection object using "context connection=true" - and attempts to open the connection. However when attempting to the Open() call inside Func2(), the code just exits. What gives? The code is pasted below, thanks!

*******THE STORED PROCEDURE**************
using System;
using System.Data;
using System.Data.SqlClient;
using System.Data.SqlTypes;
using Microsoft.SqlServer.Server;
using SqlServerProject1;

public partial class StoredProcedures
{
[Microsoft.SqlServer.Server.SqlProcedure]
public static void StoredProcedure1()
{
// Put your code here
MyClass obj = new MyClass();
obj.Func1();
obj = null;
}
};

*******THE CLASS "MYCLASS"**************
using System;
using System.Collections.Generic;
using System.Text;
using System.Data;
using System.Data.SqlClient;
using System.Data.SqlTypes;
using Microsoft.SqlServer.Server;

public class MyClass
{
public MyClass()
{

}

public void Func1()
{
using ( SqlConnection conn = new SqlConnection("context connection=true") )
{
conn.Open();

Func2();
conn.Close();
}
}

public void Func2()
{
using ( SqlConnection conn = new SqlConnection("context connection=true") )
{
if ( conn.State != ConnectionState.Open )
conn.Open();

if ( conn.State == ConnectionState.Open )
conn.Close();
}
}
}