Yenchun Chen, a Queens man accused of trying to sell fentanyl and crystal methamphetamine to an undercover officer, was being held at Rikers Island last month when he complained about chest pains, according to authorities.

He spent several days at Mount Sinai Beth Israel in Midtown Manhattan, where he was guarded by two Department of Correction officers and received occasional visitors. On the afternoon of Aug. 9, according to the police, Mr. Chen — all 6-foot-3 and 250 pounds of him — slipped quietly away.

Mr. Chen, 44, told guards that he needed to shower and they permitted him to bathe alone, according to a law enforcement official with knowledge of the matter. Five minutes later they checked on him, but the shower was empty, the window was open and a rope made of knotted sheets was dangling from it, the law enforcement official said.

His escape was stealthy, but not smooth.

“He fell a significant distance,” said Joseph Kenny, assistant chief of the detective bureau.

After touching down, Mr. Chen caught a yellow cab that a friend had ordered him and fled southbound on Second Avenue toward New Jersey, officials said.

Surveillance images released by the New York police after his escape showed him sweaty and disheveled, dressed in a white shirt and khaki pants, fleeing Mount Sinai, a hospital tag around his wrist.

He was not seen again until he was found asleep at a friend’s house in Long Island City early Tuesday, the police said. He had spent the preceding month couch surfing at the homes of friends and relatives, Chief Kenny said.

Officers from the intelligence bureau at the Department of Correction and the U.S. marshals apprehended Mr. Chen at 6:15 a.m. and took him to Bellevue Hospital for treatment.

“He’s got some injuries to his ribs and legs,” Chief Kenny said. “He’s able to walk but he’s banged up quite a bit.”

Mr. Chen is being represented on the drug case by Brad Sage, who did not immediately respond to a message for comment late Tuesday afternoon. Mr. Chen had been held on $50,000 bail, according to the office of the city’s special narcotics prosecutor, which was assisting the Drug Enforcement Administration in the case.

On Tuesday, Mr. Chen was charged with escape, the police said.

Mr. Chen fled about three weeks before Danelo Cavalcante, a Brazilian national who had been convicted of murder, escaped Chester County Prison by crab-walking up the walls.

Surveillance video shows Mr. Cavalcante wedging himself between two opposing walls and propelling himself upward to the prison roof. He ran across the roof, scaled a fence, pushed his way through more razor wire, and has proved elusive ever since.

Residents of Chester County have been told to stay inside and bolt the doors. On Monday, a homeowner said he shot at Mr. Cavalcante after he got into his garage. Mr. Cavalcante fled, armed with the homeowner’s .22 caliber rifle he had found leaning in a corner.

Mr. Chen’s time in hiding was less eventful, according to the police. He spent several weeks traveling from New Jersey to Virginia, then back to New Jersey, before he finally ended his journey in Long Island City. Following his escape, he obtained a cellphone and the police used it to help track his movements and capture him, Chief Kenny said.

The two officers responsible for guarding Mr. Chen when he escaped were suspended for 30 days without pay, according to the Department of Correction.