By Monday, the police in a small New Jersey town had gotten an anonymous tip about a body being stored in a shed outside one of the state’s largest nursing homes.

When the police arrived, the corpse had been removed from the shed, but they discovered 17 bodies piled inside the nursing home in a small morgue intended to hold no more than four people.

“They were just overwhelmed by the amount of people who were expiring,” said Eric C. Danielson, the police chief in Andover, a small township in Sussex County, the state’s northernmost county.

The 17 were among 68 recent deaths linked to the long-term care facility, Andover Subacute and Rehabilitation Center I and II, including two nurses, officials said. Of those who died, 26 people had tested positive for the virus.