Police Clearance Certificates
An often requested item for immigration purposes is a Police Clearance Certificate.
This document goes by many names. Typical names include Criminal Record Check or a Certificate of Good Conduct.
The document issued in the US is issued by the FBI and is known as a Identity History Summary.
This link provides information on ordering online or via mail. This process includes a check of your fingerprints, either through a hard card (physical paper where your fingerprints are recorded) or electronically.
The procedure prior does not include storage of the fingerprints nor reference to FBI or other federal fingerprint databases.
Note that ordering this document from outside the USA is extremely difficult due to the fingerprinting requirement.
The results that are mailed back to you then need to be forwarded to US Department of State Office of Authentications for an apostille or authentication.
If you have resided on a permanent basis in other countries than the USA, you may need to obtain similar police certificates. Refer to the national law enforcement agencies of those countries for their procedures.