SEOUL, South Korea — South Korea’s Constitutional Court, which will decide whether President Park Geun-hye is permanently removed from office, on Thursday ordered Ms. Park to respond to one of the most contentious accusations against her: that she neglected her duties on the day in 2014 when hundreds died in the sinking of a ferry.

Ms. Park’s presidential powers have been suspended since Dec. 9, when the National Assembly voted to impeach her. The Constitutional Court has until June to decide whether her impeachment is justified, either reinstating her or formally ending her presidency. Thursday’s hearing, which Ms. Park did not attend, was the start of that process.

The legislature accused Ms. Park of a wide range of violations of law and the Constitution, including taking bribes from businesses. But for South Koreans, perhaps the most emotional accusation is that Ms. Park failed to protect citizens’ lives on April 16, 2014, the day the Sewol ferry sank off the country’s southwestern coast. More than 300 people drowned, most of them teenagers on a school trip, and the country was scarred by the catastrophe, perhaps the worst in its peacetime history.

Ms. Park has been dogged by questions about what she was doing during the first seven hours of the Sewol disaster. She did not emerge from her official residence during that time, and her office has not explained what she was doing, though it has said she received updates and gave orders. In its impeachment bill, the National Assembly said Ms. Park’s reticence undermined the people’s right to know about the government’s activities.