**Core Concept**
The parietal peritoneum covering the diaphragm receives sensory information via the phrenic nerve, which primarily transmits motor signals to the diaphragm. This unique arrangement allows for the referral of pain from the peritoneum to the diaphragm and potentially to other structures via the phrenic nerve.

**Why the Correct Answer is Right**
In the case of peritonitis in the parietal peritoneum on the inferior surface of the diaphragm, pain is referred to the dermatome corresponding to the phrenic nerve. The phrenic nerve arises from the cervical spine (C3-C5) and innervates the diaphragm, as well as the parietal peritoneum covering the diaphragm. As a result, pain from the peritoneum is referred to the same dermatome as the phrenic nerve, which is typically the 3rd to 5th intercostal spaces on the anterior chest wall. This is because the phrenic nerve carries both motor and sensory information from the diaphragm and its surrounding peritoneum.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the phrenic nerve does not innervate the diaphragm's peripheral structures, such as the peripheral diaphragm or the peripheral pleura. The phrenic nerve only innervates the central diaphragm and the peritoneum covering it.
* **Option B:** This option is incorrect because the intercostal nerves (T1-T12) primarily innervate the intercostal muscles and the parietal pleura, not the diaphragm or the peritoneum covering it.

**Clinical Pearl / High-Yield Fact**
In clinical practice, it's essential to recognize that pain from the peritoneum covering the diaphragm is referred to the dermatome corresponding to the phrenic nerve (C3-C5). This can lead to atypical pain presentation in patients with peritonitis, particularly if the pain is localized to the chest wall rather than the abdomen.

**✓ Correct Answer: D. D**