I do not practice in your state, but I can give you a general answer. Not all assisted living facilities are operated by the state, in fact a good number of them are privately owned and operated. However, in most states, all assisted living facilities are subject to regulation by the state, and often by the federal government as well. So even a privately owned assisted living facility will usually have to follow state rules and regulations in order to operate legally.
Every state is different; however, most states have some regulatory oversight for these facilities.
The vast majority are privately owned. Very few states operate any assisted living homes. Also very few states provided any type of financial assistance for residences of assisted living homes.