Pat and Stuart Keel-Diffey, both 80, were found at their home in Stoke Gabriel, Devon, after emergency services were alerted on Friday.
Mrs Keel-Diffey, an author and artist, was taken to hospital after taking a suspected drug overdose.
Police are not looking for anyone else in relation to the death. The couple were said to have been in poor health.
Devon and Cornwall Police said it appeared the couple had "sought to take their own lives".
'Very lonely'
Susan Hartopp, who lives near the couple, said the community would be shocked.
"They are quite a well-known couple. It's just very, very sad.
"I know they had been poorly, or not in good health. It can be very, very lonely if you are poorly," she said.
"There will be people who may say probably we could have done more."
According to local reports, Mr Keel-Diffey was a retired vet.
Mrs Keel-Diffey is believed to suffer post-polio syndrome and uses a wheelchair.
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