Variable declaration in c# switch statement

switch (Type)
{
    case Type.A:
            string variable = "x";
                break;
    case Type.B:
            string variable = "y";
                break;
}

switch (Type)
{
    case Type.A:
            {
            string variable = "x";
            /* do other stuff with variable */
            }
            break;

    case Type.B:
            {
            string variable = "y";
            /* do other stuff with variable */
            }
            break;

}

switch (Type)
{
string variable;

    case Type.A:
            variable = "x";
                break;
    case Type.B:
            variable = "y";
                break;
}