State, county and municipal (city) employees work, respectively, for those distinct divisions of government. All are public employees, however, since all work for government, at some level.
Without looking up the codes, I'd say that only a handful of County employee's are actually considered State employee's.
The County employee's that which department is a State Agency are State...
There are certain occupations where this would be frowned upon and in some cases prohibited. Some military services for instance, especially if the ranks vary greatly. There are, generally, no other...