Put the connection string in web.config say and then access it as following
protected void ddlConnections_SelectedIndexChanged(object sender, EventArgs e)
{
string conString = "";
if (ddlConnections.SelectedItem.Value == "2013")
{
conString = ConfigurationManager.ConnectionStrings["ConString_2013"].ConnectionString;
}
if (ddlConnections.SelectedItem.Value == "2014")
{
conString = ConfigurationManager.ConnectionStrings["ConString_2014"].ConnectionString;
}
SqlConnection con = new SqlConnection(conString);
con.Open();
}