Simplifying dictionary of constant values
Your code is short, readable and efficient, so I don't think it needs much improvement. And I don't think adding a static class would give you anything (although changing the field and the method to static could make sense).

Another way to write your code would be to use switch, but I'm not sure whether it's more readable (although it could be slightly more efficient):

public string GetRefStat(string pk)
{
    switch (pk.Substring(2, 2))
    {
    case "00":
        return REF.MenuType;
    case "01":
    case "02":
    case "03":
    case "06":
        return REF.ReferenceStatus;
    default:
        throw new InvalidOperationException();
    }
}