After much searching I finally found the answer. You can change the current database for an open SqlConnection very easily:
connection.ChangeDatabase("YourDB");
An example:
private static void ConctDatabase(string connectionString)
{
using (SqlConnection conn = new SqlConnection(connectionString))
{
conn.Open();
MessageBox.Show("Database: {0}", conn.Database);
conn.ChangeDatabase("Northwind");
MessageBox.Show("Database: {0}", conn.Database);
}
}