My question came from having spent half a day of trying to make this work, but I kept getting the wrong connection when deploying (where I use another database).
My problem was, that I was using
My.Settings.DefaultConnectionString
...To retrieve the connectionString in my VB Class Library.
After following tvanfossons anwer, I dug around some more and found out, that I can simply use (after referencing system.configuration) :
System.Configuration.ConfigurationManager.ConnectionStrings.Item("DefaultConnectionString").ConnectionString
It looks in the web-config for webapplications and app.config for windows/class library apps.
I am glad it now works, but even more glad I know why. ;)