The couple were married in 2019 and had a tree removal company called TRS Tree Management.
Stacy Mair, who was from Falkland in Fife, was a director of the firm before she resigned from the role in January.
Police Scotland said Jim Mair’s death was being treated as unexplained pending the results of a post-mortem examination, but said there was nothing to suggest anyone else was involved.
Det Ch Insp Laura Young, of the force’s major investigation team, said: “Our thoughts remain with the families of those affected by this incident.
“They are understandably devastated and we are providing them with support through specialist officers at this incredibly difficult time.”