The manager of Parkside Towers, 8380 Pearl Rd., reported finding blankets and a makeshift kitchen in the rear of the property, near the playground, Sept. 28.
A large white German shepherd has also been running around the area; it's not known whether the two things are related.
Police found a blanket and pillow that looked like they had been there for awhile, a report said.
The manager said residents have become leery about going to that area because of it.
The apartment employees will clean up the area, and police said they would put the property on special attention.
The animal warden has been trying to catch the dog for a week. It's been sighted in the area a number of times.
It's not the only report of homelessness in Strongsville in recent months.
Earlier this year, police found someone living in a bunker off Mohawk Drive. And last winter, management at Royalton Greens apartments found someone was sleeping in a carport.