C# constructors with same parameter signatures

You can used the named constructor idiom:

public class Thing
{
    private string connectionString;

    private string filename;

    private Thing()
    {
        /* Make this private to clear things up */
    }

    public static Thing WithConnection(string connectionString)
    {
        var thing = new Thing();
        thing.connectionString = connectionString;
        return thing;
    }

    public static Thing WithFilename(string filename)
    {
        var thing = new Thing();
        thing.filename = filename;
        return thing;
    }
}