I never had to take a course entitled "New York History". I learned a good deal of state history through my US History courses (you can't discuss the Revolutionary War without mentioning NY), but I never had a dedicated semester or year of state history.
It is possible that students in the public elementary schools get a semester or year dedicated to state history. I attended Catholic school through 5th grade... they didn't care how much history (or anything else) you knew as long as you could recite the Lord's Prayer correctly.
(Not knocking Catholic schools in general, some of them are excellent... mine just happened to suck.)