What type of criminal background check document is required for the non-immigrant O-A visa for US citizens and how should it be authenticated?

Question for US citizens who have done the non-immigrant O-A visa: For the criminal background check document, the guidelines seem loosey-goosey. Can anyone clue me in on whether to get a local police report, state police report or FBI report (or government-approved FBI channeler)?

Also, how did you get it authenticated? I keep getting different stories and the process is not clearly stated on the Thai Embassy website. The nycourts.gov rep described a process that seems overly complicated involving couriers and visits to the NYC Supreme Court offices for authentication. Thanks!