I have built a Windows Phone Application using SQL Server CE database.
We need transplant this app to Windows 8 Metro Style.
Do Windows 8 Metro-style applications support SQL Server CE local databases?
As already answered by ErikEJ, there is no native support for a local SQL Server CE database, but maybe this third party component SQLite is usefull for you?
Tim Heuer has wrote a blogpost about how to use SQLite in a metro style app: http://timheuer.com/blog/archive/2012/05/20/using-sqlite-in-metro-style-app.aspx
In the blogpost there is also a video with the "How to" steps to use SQLite in your app.
No, currently Microsoft does not provide a local database for Metro applications with C# and XAML.
Not only can you not connect to a local SQL database, you can't connect to a remote one either. Everything has to go through web services... or use SQLite.
来源：https://stackoverflow.com/questions/10909202/do-windows-8-metro-style-application-support-sql-server-ce-local-database