Police said they attended an incident at a care home in Argyll and Bute at the end of January following a call relating to a woman.
An 82-year-old man, reported to have been a visitor at Auchinlee care home on Campbeltown, has now been reported to Scotland's procurator fiscal.
The home, which cares for residents over the age of 65 with dementia, is run by CrossReach, a Church of Scotland body.
A Church of Scotland spokesman said: "We reported the matter to Police Scotland and the social work department.
"It would be inappropriate to make any further comment while investigations are continuing."
A police spokesman said: "An 82-year-old man is subject of a report to the procurator fiscal in connection with alleged sexual offences."
The Care Inspectorate said the care and well-being of residents is its top priority.
"We have been notified of an allegation of a serious incident at this service and are working closely with colleagues at Police Scotland and other partners," a spokesman said.
"We are being kept fully informed and are monitoring this care home closely.