My local rental didn't have that movie (I'm assuming it's either "Day of the Dead" or "Day of the Damned"), so if you could characterize the zombies in it I'd be grateful (While I prefer first hand knowledge in my studies, if it is unattainable I will gladly accept second hand accounts).
ITT: Like most have already said, it depends of the Zombie Breed or Type. Some zombies have shown remarkable amounts of both agility and intelligence, particularly the "Ragies" of 28 Days Later (also, already said). Also, if a zombie knows where you are their attempts to catch you would most likely be relentless, given that most known zombie types continue to attack even when completely cages or otherwise held back. This leads me to believe that even a less agile or intelligent zombie could, given time, potentially climb to any point you inhabit if gone unchecked for any extent of time.
Thus, even if you have a secured, high vantage point I recommend keeping a close watch on any means of ascension, even if it's a rock face or straight ladder. Best be prepared for the worst case scenario in any event.