“Does the state of NY still have the death penalty?”
No. The New York Court of Appeals ruled that the jury instructions required by New York’s Death Penalty statute were unconstitutional. Specifically, the law required a jury to unanimously choose either death or life without parole in a capital case — and if the jury was not unanimous, there would be an automatic sentence of life with the possibility of parole after 20 years. This bizzarre rule meant that if a jury was evenly divided between death and life without parole, a defendent would get a more lenient sentence than either possibility! The court overturned the statute on the basis of due process provisions of the New York State Constitution and is therefore unappealable. The legislature could modify the instructions by statute, but it has not chosen to do so.
And there is a serious halachic issue with the death penalty as it is administered in the United States, as the gemara in Sanhedrin 57a requires eyewitness testimony even in a Noachide court. Rambam brings this down as halachah in Hilchot Melachim 9:14. However, in the United States you can convict and give any penalty, including death, based on circumstantial evidence. I’ve had multiple rabbis tell me that because of issues like this, Jews should not serve on juries in capital cases in the United States.