This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
In general the rule is that you should assume that a class is not designed to be used by multiple threads, unless the docs specifically say it is. It's true that some docs specifically tell you when a class isn't thread-safe, but that's not really necessary. There are also a few classes which are really thread-safe even though the docs don't say so, but you generally can't rely on that. The default is that classes are not thread-safe unless it's otherwise stated.