Charmain Adusah, 41, was found lifeless in the bath of a hotel room in the city of Koforidua in March 2015.
Her husband Eric Adusah was charged with her murder but the court case collapsed due to a lack of evidence.
A post-mortem examination in Ghana concluded she died of a heroin overdose.
Her family dispute this finding.
A second post-mortem eight months later in the UK found no evidence of assault.
The UK inquest was held at Essex Coroner's Court in Chelmsford.
Mr Adusah asked Home Office pathologist Charlotte Randall, who conducted the second post-mortem examination: "Is there any way you could find out how it got in the body?"
He continued: "I wasn't there, but my name has gone everywhere and I have no idea what happened. I don't know how it got in her body.
"My wife never took that in the house. I never saw her do anything like that."
Senior Essex coroner Caroline Beasley-Murray rejected possible conclusions of unlawful killing, suicide and accidental death.
She said: "Because there wasn't sufficient evidence for any of these possible conclusions, I'm going to return an open conclusion.
"We shall never quite know what happened. There just isn't the evidence."
Ms Adusha, whose  maiden name was Speirs, had lived in Rayleigh, Essex, but was originally from Arbroath in Angus.
She had family in Scotland and spent several years in Swansea where she worked for the NHS.
A UK inquest for a Scottish woman whose death in Ghana prompted a murder investigation has recorded an open conclusion.