A homeowner on John Street saw a large tan cat in his backyard at 11:30 a.m. on Sunday.
It was also observed by four other members of his family.
Their property backs up to the Audubon Society's property.
The cat was described by the family as a Mountain Lion.
The Connecticut Department of Environmental Police was contacted.
Representatives of the DEP responded and with assistance of the Greenwich Police Department, looking for signs of the animal.
Police say the animal did not make contact with any people or pets.
The Audubon Society has chosen to close their trails until further notice.
On Saturday, a different mountain lion was killed in an auto accident.
Police said a 2006 Hyundai Tucson SUV collided with the big cat around 1:00 a.m. on Saturday on Wilbur Cross Parkway in the area of Exit 55 in Milford.
The mountain lion died due to injuries sustained during the collision, officials said. The driver of the vehicle was not injured.
The 140-pound male mountain lion was been transferred to a DEP facility for further examination. The large cat may be the one sighted in Greenwich on Sunday, June 5.
The Connecticut DEP has been cooperating with the Town of Greenwich Police Department to investigate recent sightings of a large cat in the King Street area of Greenwich. Based on photographs taken of the animal and other evidence it appeared that the animal was a mountain lion.
Mountain lions can travel long distances and may have found its way to Milford, about 40 miles away, official said.
There is no native population of mountain lions in Connecticut and the eastern mountain lion has been declared extinct by the U.S. Fish and Wildlife Service. DEP officials have speculated that the animal escaped from a handler or was released.
This incident is still under investigation by DEP EnCon Police, part of which will be to determine if in fact the cat killed in the collision is the same cat seen in Greenwich.