Yes, you should give tort claims notice of claim before filing suit.
Do you have your children back yet? Sounds like the bigger problem is the neglect action and the likely dependency proceedings. You should act first to secure your children, restore your custody rights and conclude your issues with ACS and the Police before you trying to sue them. If you sue them while your children-related issues are still going on, you're likely to frustrate the outcome of your case.... Call if you need help. Good luck.
Without addressing the merits of your claim, the answer to your question is yes, under NY law you have to file a notice of claim before suing ACS and the NYPD. Suing these entities is a very complicated task. There are many intricacies of this area of the law that are pitfalls even for attorneys who practice in this area, causing the cases brought to be dismissed. As an example, the NYPD is a department of the City of New York, thereby making the City of New York the proper entity upon which to serve a notice of claim, not the police department. It is best to consult with an attorney who is well versed in this area of the municipal law so that your case does not get dismissed on a technicality. Furthermore, you should be aware of the very short time limitations within which to make a claim against the City of New York or other related municipalities. Some time frames within which to sue are as short as 30 days.