法院文件應該不用經過本地公證，可以直接認證

美國北京大使館說：

http://beijing.usembassy-china.org.cn/acs_notary.html

Authentication
Please make sure the documents you bring to us have already been authenticated by the Notarization and Authentication Division of Consular Affairs Department of the Chinese Ministry of Foreign Affairs. The telephone number of the Notarization and Authentication Division is (8610) 6588-9761.

一般三級認證是私人簽字的聲明合同。中國法院的判決，如果是蓋章的原件，應該不用去公證，可以直接去中國外交部認證後，然後到美國領事館認證。你可以向中國外交部認證機構打電話詢問。

美國外交部如是說：比大使館說得詳細一些。
http://travel.state.gov/content/passports/english/abroad/events-and-records/divorce/divorce-legal-issues.html