在Cayman Islands政府网站上看的信息不太确定我理解对了:
http://www.immigration.gov.ky/portal/page/portal/immhome/visitinghere/visas/visitorsvisas/visarequiredcountries
如果是中国护照,这个是可以免签证的:you are resident in the United States of America; and you arrive directly from that country; and you produce on arrival a valid United States Alien Registration Card; and you produce on arrival a return or round trip ticket to the United States.
没有特别指美国永久居民。不知道Alien Registration Card是什么。多谢!