Inside the JDK folder there is a file called src.zip. This contains the source for most of the classes in the API.
But let me save you the trouble of looking it up. Most public methods are synchronized. The store methods aren't, but they use synchronization internally. getProperty also isn't synchronized but it uses super.get which is synchronized. All in all, the API says
This class is thread-safe: multiple threads can share a single Properties object without the need for external synchronization