**Core Concept**
Meningitis due to H. influenzae can cause permanent neurological damage, particularly to the auditory nerve and brainstem, leading to hearing loss and other neurological sequelae. Early detection and intervention are crucial to prevent long-term complications.

**Why the Correct Answer is Right**
Bilateral evoked auditory response (BAER) testing is essential in patients with meningitis due to H. influenzae to assess for potential hearing loss, which can occur even in the absence of overt clinical symptoms. BAER testing measures the electrical activity of the auditory nerve and brainstem in response to auditory stimuli, providing an objective assessment of hearing function. This is particularly important in patients with H. influenzae meningitis, as hearing loss can be a significant and irreversible complication.

**Why Each Wrong Option is Incorrect**
**Option A:** EEG (electroencephalogram) may be used to assess for seizures or encephalopathy in patients with meningitis, but it is not the primary test for detecting hearing loss.
**Option B:** Assessing developmental milestones is an important aspect of follow-up care, but it is not a specific test for detecting hearing loss.
**Option D:** Referring for physiotherapy may be necessary in some cases of meningitis, particularly if there are concerns about muscle weakness or other motor deficits, but it is not a relevant step in the discharge process for this patient.

**Clinical Pearl / High-Yield Fact**
Patients with meningitis due to H. influenzae are at risk of developing hearing loss, which can be permanent and irreversible. Early detection through BAER testing is crucial to prevent long-term complications.

**Correct Answer:**
✓ Correct Answer: C. Bilateral evoked auditory response.