variable chapter c# switch statement

why c# switch statement, non-static used churned cases, wholly announce initial case?

for example, following throws blunder "a internal non-static named 'variable' already tangible scope".

switch (type)
{
    box type.a:
            twine non-static = "x";
                break;
    box type.b:
            twine non-static = "y";
                break;
}

however, per logic, initial chapter should strike form type.b. variables within switch matter exist unparalleled scope, created/allocated before any explanation processed?