Is this a federal claim or a state civil rights claim? If you plan on suing the NYPD and/or the City of NY, you are going to need a lawyer, because a §1983 Civil Rights claim in federal court, or a state civil rights claim have very strict guidelines on filing times, manner of service, and so forth.
DO NOT TRY TO SUE THEM ON YOUR OWN.
If you are already being represented in a criminal matter, and want to try to use this as a defense, speak to your defense attorney (or make sure you are appointed counsel), and if you have already had a criminal charge dismissed, then speak to the attorney who helped you get the charges dismissed about a good civil rights attorney.
This does not constitute legal advice or the engagement of my services as an attorney.
You do not have to serve a Notice of Claim on the NYPD - you only serve and sue the City of New York.
The above answer, and any follow up comments or emails is for informational purposes only and not meant as legal advice.