I am working on a C# 4.0, WPF 4.0, SQL 2008 project and I do work at home and in the office. I just setup SubVersion using Visual SVN per the recommendations found in other ques
In source control, use the connection string in app.config that is used for the most commonly used connection string (likely to be work).
At home, hijack (or checkout) the file that selects which connection string to use, and edit it to use your home connection string.