If you must show an ID to NYPD (the police), you can use the IDNYC. The IDNYC is a picture ID issued by the City of New York that does not include place of birth or nationality. Use this ID instead of a passport or ID from another country.

Showing an ID to NYPD may result in you receiving a ticket and avoid being fingerprinted. However, if you are arrested by the NYPD,  your fingerprints will be automatically shared with ICE.