NY is one of the communist states that don't allow private blood testing due to state insurance and medical billing laws. it used to be you could cross the border to CT or PA and get it done but they've changed their requirements recently. I know someone from NJ who came to CT and had it done but he was lucky he didn't get asked for ID.
PPWC, I too live in CT and we dont get asked for ID bc our state allows provatge blood testing.