I have created a console application and an app.config file and Connections.config file. The app.config file has a connectionstring property source pointing to the Connectio
MSDN says:
Do not include any additional elements, sections, or attributes.
You need to remove the XML encoding.
Edit
Also, you need to set the properties of your config file to Copy to Output Directory = Copy if newer or Copy always.

Edit 2
To build on what Dave said, you add the clear element to your external file. Your final Connections.config file should look exactly like this: