In New York State, a background check or certificate of good conduct is issued by local police departments (ie NYPD) and the New York State Department of Criminal Justice. The local police department should be able to notarize the letter of conduct; the NYPD letter of conduct should be signed by a Public Inquiry & Request Section's supervisor, no notary is necessary. The NYS DOJ should send you a notarized letter signed by an Identification Specialist. Obtaining a certificate of conduct generally entails capturing of fingerprints by a designated center. If you have already left the country, it is still possible to submit a fingerprinting card attested by a foreign local police or US Consulate.
RELATED DOCUMENTS: a certificate of good conduct from the FBI is sometimes required in addition or in lieu of the State documents. We suggest that you contact an approved FBI Channeling Agency.
Related resources: Certified Translation