Can you have cranial nerve damage with face lacerations?

Yes. If a cranial nerve is injured in the face, it is usually either the trigeminal (#5) or facial (#7). Depending on where the laceration is, sometimes these nerves require repair, other times they can be left to re-sprout in the area.
Yes. You can easily have injury to the facial or trigeminal nerve with facial lacerations. Other cranial nerves can also be involved, though these are the cutaneous nerves, and more easily damaged with superficial injuries.

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Cranial nerve damage possible from face laceration?

The cranial nerves . And there are 12, arise in the pons, midbrain and brain stem. The facial laceration is likely to severe/injue branches of vii, the facial nerve, providing innervation of facial muscles. Read more...