C#
using(SqlConnection c = new SqlConnection
      ("context connection=true")) {
  c.Open();
  // do something with the connection
}
Visual Basic .NET
Using c as new SqlConnection("context 
   connection=true")
  c.Open()
   ' do something with the connection
End Using 

In order to see whether your code is actually running in the same connection as the caller, you can do the following experiment: use a SqlConnection object and compare the SPID (the SQL Server session identifier) as seen from the caller and from within the connection. The code for the procedure looks like this:

C#
using System.Data;
using System.Data.SqlClient;
using Microsoft.SqlServer.Server;
public partial class StoredProcedures {
 [Microsoft.SqlServer.Server.
   SqlProcedure()]
 public static void SampleSP(
    string connstring, out int spid) {
  using (SqlConnection conn = 
    new SqlConnection(connstring)) {
   conn.Open();
   SqlCommand cmd = new SqlCommand
     ("SELECT @@SPID", conn);
   spid = (int)cmd.ExecuteScalar();
  }
 }
}


Visual Basic .NET
Imports System.Data
Imports System.Data.SqlClient
Imports Microsoft.SqlServer.Server

Partial Public Class StoredProcedures
  <Microsoft.SqlServer.Server.SqlProcedure()> _
  Public Shared Sub SampleSP(ByVal
    connstring As String, ByRef spid 
    As Integer)
   Using conn As New SqlConnection
    (connstring)
    conn.Open()
    Dim cmd As New SqlCommand
     ("SELECT @@SPID", conn)
    spid = CType(cmd.ExecuteScalar(),
           Integer)
   End Using
  End Sub
End Class