If you're through a consulting company that sells your time to the state and managed like an employee then you're not an employee of the state. You're an employee of that consulting company. The arrangement between the state and your employer is one thing, and your arrangement with the consulting company is another. Your company can't sell your time on a regular schedule to the state and then tell you you're a contract employee. That doesn't mean the state can't contract for a company's employees to be assigned to work on-site at the state's offices, though.
If you're on contract with the state directly, then they should treat you like a contractor. If they manage you as an employee, they need to employ you internally. If they want to keep you as a contractor, they should give you those freedoms.
You need to know that this isn't just about you. Allowing yourself to be treated as an employee and compensated as a contractor weakens everyone else's position, too. In fact, there's probably a union like AFSCME that would be very interested to talk to you about this.