The inquiry is looking into allegations of an alleged incident at Laburnum Court in Lower Broughton, Salford.
The home cares for up to 68 elderly people and provides specialist care for residents who have dementia.
Four Seasons Health Care, which runs the home, said its manager had reported a relative's concerns to authorities.
A spokeswoman for the Wilmslow, Cheshire-based company, which runs 400 homes across the UK, also said: "When concerns were raised by a relative about the conduct of a member of staff towards a resident the home manager notified Care Quality Commission, safeguarding and the police so that the concern could be investigated in an unbiased and transparent way.
"We are also co-operating actively in a separate police investigation that was initiated after a member of staff and a resident discovered apparent financial irregularities at the home."
Salford City Council said it is "confident appropriate measures" are in place at the home, adding that it will work closely with all relevant agencies.
"The investigation is in the early stages so we cannot comment further at this stage."
Greater Manchester Police said it was "called to a care home in the Salford area on 7 April following reports a resident had been assaulted".
A recent inspection by the Care Quality Commission rated the home as requiring improvement.
Police and social services are investigating claims that a staff member assaulted an elderly resident of a care home in Greater Manchester.