The code:
var db = new dbContext();
Console.Writeline(db.Database.Connection.ConnectionString);
always works. So, if you created an entity model from your database and used the DbContext Generator T4 template, you can still use it.
ObjectContext API, :
var connection = context.Connection as EntityConnection;
if (connection == null) throw new ...;
var storeConnectionString = connection.StoreConnection.ConnectionString;