It's not automatic in C++/CLI. You have to set it up manually. Start by Add New Item, Utility, Configuration File. That will create the app.config file in your solution. It should also open the app.config xml file in the editor window. Unfortunately, there's no nice editor, but the intellisense is familiar with the format. For a connection string,
<add name="MyConnString" profidername="System.Data.SqlClient" connectionstring="connString" />
Next, edit the project you want to use the connection string in and add a reference to System::Configuration. (Remember to add the using namespace in the file.) Then in your project's properties, edit the Build Events, Post-Build Event, and add the command line
copy app.config "$(TargetPath).config"
That will copy the app.config file to yourAppName.exe.config during the build.
Finally, to get the connection string use this:
ConnectionString ^localDb = ConfigurationManager::ConnectionStrings["MyConnectionString"];