I would draw a raycast line between the zombie and the player. If the zombie has clear sight of the player AND the line is less than say… 2 units, then have the AI do a melee attack (google unity melee tutorial to find out the specifics of implementing this, one method to get the distance between 2 objects is found here: http://forum.unity3d.com/threads/37918-Distance-between-two-objects). This melee attack should check to see what type of object it has hit. If it has hit the player object, you can use SendMessageUpwards() to send a message to the player object to say “apply damage” and also how much damage to apply.
Here is a video tutorial of building a raycast gun. It’s not specifically what you want, but it tells you the details of how to give damage to another object. You may need to watch part 011, 012, and 013. I’ve forgotten where the damage specific stuff is.