I think it depends on the place of this word. For example, try to get the difference : Это решённый вопрос. Этот вопрос решён.

Unfortunately I didn't find any rules for this case.

I've found an explanation: "When you use 'am/is/are' in English, it's a short form in Russian, when you don't, it's a full one. In most cases this could work" (http://learn-russian.livejournal.com/724836.html). Short forms function as predicates. Read this: http://www.alphadictionary.com/rusgrammar/pastpass.html