Contractors curious about an extension cord on the roof of a Michigan grocery store made a startling discovery: a 34-year-old woman was living inside the business sign, with enough space for a computer, printer and coffee maker, police said.

“She was homeless,” said Brennon Warren, an officer with the Midland police department. “It’s a story that makes you scratch your head, just somebody living up in a sign.”

The woman, whose name was not released, told police she had a job elsewhere but had been living inside the Family Fare sign for roughly a year, Warren said. She was found on 23 April.

Midland, best known as the global home of Dow Inc, is 130 miles (209km) north of Detroit.

The Family Fare store is in a retail strip with a triangle-shaped sign at the top of the building. The sign structure, probably 5ft (1.5 meters) wide and 8ft (2.4 meters) high, has a door and is accessible from the roof, Warren said.

“There was some flooring that was laid down. A mini desk,” he said. “Her clothing. A Keurig coffee maker. A printer and a computer – things you’d have in your home.”

The woman was able to get electricity through a power cord plugged into an outlet on the roof, Warren said.

There was no sign of a ladder. Warren said it’s possible the woman made her way to the roof by climbing up elsewhere behind the store or other retail businesses.

“I honestly don’t know how she was getting up there. She didn’t indicate, either,” he said.

A spokesperson for SpartanNash, the parent company of Family Fare, said store employees responded “with the utmost compassion and professionalism”.

“Ensuring there is ample safe, affordable housing continues to be a widespread issue nationwide that our community needs to partner in solving,” Adrienne Chance said, declining further comment.

Warren said the woman was cooperative and quickly agreed to leave. No charges were pursued.

“We provided her with some information about services in the area,” the officer said. “She apologized and continued on her way. Where she went from there, I don’t know.”

The director of a local non-profit that provides food and shelter assistance said Midland – which has a population of 42,000 – needs more housing for low-income residents.

“From someone who works with the homeless, part of me acknowledges she was really resourceful,” said Saralyn Temple of Midland’s Open Door. “Obviously, we don’t want people resorting to illegal activity to find housing. There are much better options.”