java - static method is implicitly thread safe?

One of my java static method is accessed by multiple threads . Do I need to synchronize the method explicitly by synchronized keyword?.

Sometime back I read in a book which states that

static method is implicitly thread safe as the method is not object specific

.

Well known example is , Singleton implementation. In which getInstance() is static and do we need to mark this as synchronized as well?

 public synchronized static Logger getInstance() {
         if( instance == null ){
             instance = new Logger();
         }

         return instance;
     }

Thanks