It comes after a jury concluded the death of a man from St Austell was suicide, while undergoing care 140 miles from where he lived.
David Knight was killed by a train near St Austell after going on leave from a Somerset hospital.
The Department of Health has admitted "unacceptable" patients "are receiving care far from home".
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BBS South West Political Reporter Tamsin Melville said county coroner Dr Emma Carlyon was understood to be satisfied there was a commitment locally to continue to work hard to ensure the lowest number of patients possible leave the county for treatment.
An inquest in June heard that in May last year Mr Knight died of multiple injuries when he was hit by a train on the viaduct.
The 29-year-old had been suffering from paranoid schizophrenia when he died.
A jury said his death was contributed to by an inadequate risk assessment and support while he was on leave from Cygnet Hospital in Kewstoke, Somerset.
The inquest heard Mr Knight was being treated there because there were no acute psychiatric inpatient beds available in Cornwall.
The NHS said 30 adult mental patients were placed out of Cornwall in 2015/16, 150 the year before when a key unit was closed for six months, and 60 the year before that.
The Department of Health said it had increased mental health funding to Â£11.7bn and had accepted the recommendation of the Mental Health Taskforce that the inappropriate use of out of area treatments for adults in acute care "must be eliminated by 2020/21".
"We will work to a faster timetable if at all possible," said a spokeswoman.
"We will consider Dr Carlyon's letter in detail once it arrives."
Cornwall's coroner will raise concerns with the health secretary over the care of mentally ill patients far from home.