For a zoo to let a leopard escape is worrisome. To lose three of them and fail to warn residents for more than two weeks seems something else altogether.

A safari park near the city of Hangzhou in eastern China is facing an onslaught of questions after it achieved that dubious feat, belatedly admitting late last week that three of its leopards had somehow absconded into the nearby hills.

By Monday, searchers had found two of the big cats, and teams with dogs, drones and dart guns were looking for the third. They brought in 90 live chickens as bait to lure out the missing one.

A search for answers was also underway. The government put a senior manager of the zoo under criminal investigation, and officials promised an inquiry. Many Chinese people wondered how the Hangzhou Safari Park could lose several wildcats and hold back the news for so long.

The safari park and the government were vague at first about when the leopards escaped, but Hangzhou officials said at a news conference on Monday that they had fled on April 19 when two caretakers cleaning their enclosure violated “operational rules” — apparently by leaving doors open.

The park’s explanation for keeping the news to itself while it secretly searched: It did not want to frighten the neighbors.

“Taking into account that the escaped young leopards were not very aggressive, and worried that disclosing the matter would trigger panic, we did not promptly disclose the news,” the safari park said in a statement on Saturday after the local government confirmed the escape and warned residents to be on guard.

The Chinese internet has been agog with updates and discussion about the missing leopards. Many people were not impressed by the park’s explanation and had questions about the government’s actions, the frantic search and the well-being of the leopards that were hunted down. Leopards are an endangered species, and are found in the wild across remnant patches of western China.

“The ‘leopard hiding’ affair has exposed gaps in management that warrant more scrutiny and reflection,” Chinese Central Television News opined in an online article.

Chen Fang, the owner of a rural leisure lodge in the area of the search, said in a telephone interview, “The zoo should have notified us earlier.”

“If you say you worried about triggering public panic, wouldn’t someone panic if they ran into a leopard on the city outskirts?” one person wrote on Weibo, the popular Chinese social media platform.

Zoos have become popular tourist destinations in China, and there have been attacks involving visitors stepping out of their cars in drive-through animal parks.

Online, many people voiced sympathy for the escaped leopards, citing signs that they had been hunted down and possibly mauled by tracker dogs.

Residents have described spotting the animals for at least a week before the zoo and the local authorities revealed that they had escaped, according to Chinese news reports.

Zhu Caifeng, a tea farmer, said he had spotted one in a field in early May. “At first I thought it was some kind of cat, but when I looked more closely, the dimensions weren’t right,” he told The Shanghai Observer. “This was much bigger than a cat.”

Mr. Zhu was alarmed but kept his cool. He used his phone to snap a picture of the creature gazing at him quizzically among the tea plants. But he was too busy with farm work to overthink encountering an exotic wildcat. After it walked off, he said, he kept working in his fields.

Mr. Zhu later made another sighting of a leopard, but friends in the village advised him not to report it to the authorities in case that brought “unnecessary hassles and interfered with work,” he said.

A day later, the thought of a leopard attacking someone led him to change his mind, and he shared his picture on WeChat, the Chinese social media service, and soon the area was abuzz. Nearby villages went on guard.

Mr. Zhu declined to be interviewed, adding that he had been overwhelmed by journalists’ calls.

“Online many have praised me for swiftly raising the alarm,” he told The Shanghai Observer. “But there are also people who accused me of making a mountain out of a molehill.”

Yet even after the sightings grew and residents called the police, managers at the Hangzhou Safari Park — and maybe the local authorities — appeared to have hoped to deal with the missing cats quietly during China’s May Day vacation. The park did not immediately answer calls seeking comment on Monday.

Chinese news reports have said that when asked by journalists, the park initially denied that any leopards were missing. It announced on Saturday that it was closing temporarily to deal with unspecified “safety issues.”

Later that day, the government of Fuyang District, the site of the park, disclosed that the three leopards had gone missing and that one was still at large; the park then issued its apologetic admission. Since then, search teams have swarmed the lush hills on the edge of Hangzhou.

So far, there have been no reports of injuries from the leopards, and the safari park and some experts said the shy, youngish cats were unlikely to attack people.

Still, Chinese news sites offered advice about what to do if you run into a stray leopard.

“Don’t look them straight in the eye,” one article said. “Whatever you do, don’t panic,” said another. If attacked, it added, consider as a last resort ramming your fist down the leopard’s throat. “That’s the only chance of saving your life.”

Liu Yi contributed research.