**Core Concept**
A base of the skull fracture involving the petrous temporal bone can lead to a specific clinical presentation due to its proximity to the inner ear structures. The petrous temporal bone houses the otic capsule, which contains the structures responsible for hearing and balance.

**Why the Correct Answer is Right**
The presence of a petrous temporal bone fracture is often associated with a perilymphatic fistula. This occurs when the fracture disrupts the thin membrane separating the perilymph from the middle ear, leading to the leakage of perilymph into the middle ear. This results in a conductive hearing loss, tinnitus, and vertigo. The perilymphatic fistula is often diagnosed through clinical examination and confirmed with imaging studies like CT or MRI.

**Why Each Wrong Option is Incorrect**
**Option A:** Cerebrospinal fluid (CSF) otorrhea is a possible complication of a petrous temporal bone fracture, but it is not the most specific or important sign. CSF otorrhea occurs when the fracture disrupts the dura mater, allowing CSF to leak into the ear.

**Option B:** Conductive hearing loss is a common symptom of a petrous temporal bone fracture, but it is not the most specific or important sign. Conductive hearing loss can result from various causes, including middle ear effusions or ossicular damage.

**Option C:** Facial nerve paralysis is a possible complication of a petrous temporal bone fracture, but it is not the most specific or important sign. Facial nerve paralysis can result from damage to the facial nerve, which runs through the temporal bone.

**Clinical Pearl / High-Yield Fact**
When evaluating a patient with a base of the skull fracture involving the petrous temporal bone, it is essential to perform a thorough neurological examination, including assessment of hearing, balance, and facial nerve function.

**Correct Answer:** C.