Sure they do, and here in NY all you got to do is go to the DMV, just like getting a driver's license, present them 6 points worth of ID including photo id, just like the driver's license, and you're set to go. Basically stone soup minus the car. In other words, in order to get one you don't really need one already.
They did come out with this Municipal ID card at least for New York City some years ago which is supposed to be easier to get... for foreigners. If you were born here like me, good luck.
Like a lot of city agencies here, the DMV is filled with GED types with a severe God Complex and a big bloody hammer aimed at groin level, and boy do they love to use it. Every time you go, they make it so you have to make a second trip to do what you came for.
Funny when people talk about how supposedly easy it is to get all this stuff here, when if it is, I sure ain't seen it.